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algebraic geometry, a stable principal bundle is a generalisation of the notion of a stable vector bundle to the setting of principal bundles. The concept of
Stable_principal_bundle
In mathematics, a stable vector bundle is a (holomorphic or algebraic) vector bundle that is stable in the sense of geometric invariant theory. Any holomorphic
Stable_vector_bundle
Type of vector bundle
{\displaystyle K} the canonical bundle over the Riemann surface M. Then a Higgs bundle ( E , φ ) {\displaystyle (E,\varphi )} is stable if, for each φ {\displaystyle
Higgs_bundle
Vector bundles theorem
Donaldson–Uhlenbeck–Yau theorem) relates stable vector bundles over a complex manifold to Einstein–Hermitian vector bundles. The correspondence is named after
Kobayashi–Hitchin correspondence
Kobayashi–Hitchin_correspondence
Study of vector bundles, principal bundles, and fibre bundles
theory is the general study of connections on vector bundles, principal bundles, and fibre bundles. Gauge theory in mathematics should not be confused
Gauge_theory_(mathematics)
Correspondsnce between Higgs bundles and fundamental group representations
of Higgs bundles in the category of principal bundles. There is a notion of a stable principal bundle, and one can define a stable principal G {\displaystyle
Nonabelian Hodge correspondence
Nonabelian_Hodge_correspondence
Mathematical parametrization of vector spaces by another space
In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X
Vector_bundle
Association of cohomology classes to principal bundles
associating to each principal bundle of a topological space X a cohomology class of X. The cohomology class measures the extent to which the bundle is "twisted"
Characteristic_class
Concept in differential geometry
Riemannian manifold, for which no principal bundle over it (with a compact Lie group as structure group) has a stable Yang–Mills connection is called Yang–Mills-instable
Stable_Yang–Mills_connection
Type of differentiable manifold
{\displaystyle p} . Equivalently, the tangent bundle is a trivial bundle, so that the associated principal bundle of linear frames has a global section on
Parallelizable_manifold
Construct in mathematics
principal H {\displaystyle H} -bundles on U {\displaystyle U} with isomorphism as morphisms (thus the category is a groupoid). As principal bundles glue
Gerbe
Partial differential equations whose solutions are instantons
of partial differential equations for a connection on a vector bundle or principal bundle. They arise in physics as the Euler–Lagrange equations of the
Yang–Mills_equations
Exact homotopy case
map X → BU(n) unique up to homotopy. A particular application are principal U(1)-bundles. This space with its universal fibration may be constructed as either
Classifying_space_for_U(n)
Algebraic geometry analog of a principal bundle in algebraic topology
In algebraic geometry, a torsor or a principal bundle is an analogue of a principal bundle in algebraic topology. Because there are few open sets in Zariski
Torsor_(algebraic_geometry)
Concept in differential geometry
{\displaystyle \|\Phi \|=1} . Stable Yang–Mills connection de los Ríos, Santiago Quintero (2020-12-16). "Connections on principal bundles" (PDF). homotopico.com
Stable_Yang–Mills–Higgs_pair
Special tangential structure
spinc structure induces a principal U ( 1 ) {\displaystyle \operatorname {U} (1)} -bundle or equivalently a complex line bundle. Every spin structure induces
Spinc_structure
Given some line bundle L on C, let S U C ( 2 , L ) {\displaystyle SU_{C}(2,L)} denote the set of isomorphism classes of rank-2 stable bundles E on C whose
Complete_algebraic_curve
Generalization of vector bundles
moduli of stable vector bundles in many specific cases, such as on principally polarized abelian varieties and K3 surfaces. A vector bundle E {\displaystyle
Coherent_sheaf
Geometric space whose points represent algebro-geometric objects of some fixed kind
the number of moduli of vector bundles and the closely related problem of the number of moduli of principal G-bundles has been found to be significant
Moduli_space
Topological space
normal bundle is flat and whose principal curvatures are constant along any parallel normal vector field. The set of isoparametric manifolds is stable under
Isoparametric_manifold
{g}}} and E ↠ B {\displaystyle E\twoheadrightarrow B} be a principal G {\displaystyle G} -bundle with a compact orientable Riemannian manifold B {\displaystyle
Bi-Yang–Mills_equations
Describes a periodicity in the homotopy groups of classical groups
much further research, in particular in K-theory of stable complex vector bundles, as well as the stable homotopy groups of spheres. Bott periodicity can
Bott_periodicity_theorem
Study of spaces with group actions
and other applications includes a naturally occurring group bundle (see principal bundle for details). Let us first consider the case where G {\displaystyle
Equivariant_topology
System of partial differential equations used in Higgs field theory
differential equations for a connection and Higgs field on a vector bundle or principal bundle over a Riemann surface, written down by Nigel Hitchin in 1987
Hitchin's_equations
Chest discomfort due to disorder of the heart muscles
this way, stable angina may be thought of as being similar to intermittent claudication symptoms. Other recognized precipitants of stable angina include
Angina
Generalisation of a sheaf; a fibered category that admits effective descent
moduli stack of principal G L n {\displaystyle GL_{n}} -bundles. Since the data of a principal G L n {\displaystyle GL_{n}} -bundle is equivalent to
Stack_(mathematics)
{g}}} and E ↠ B {\displaystyle E\twoheadrightarrow B} be a principal G {\displaystyle G} -bundle with an orientable Riemannian manifold B {\displaystyle
F-Yang–Mills_equations
Type of integrable system
system is a partial compactification of the cotangent bundle to the moduli space of stable G-bundles for some reductive group G, on some compact algebraic
Hitchin_system
Diffeomorphism that has a hyperbolic structure on the tangent bundle
unit-length vectors on H. Note that a bundle of unit-length vectors on a surface is the principal bundle of a complex line bundle. One starts by noting that T
Anosov_diffeomorphism
Mathematical concept
\mathbf {CP} ^{\infty }} is the associated vector bundle of the principal U ( 1 ) {\displaystyle U(1)} -bundle S ∞ → C P ∞ {\displaystyle S^{\infty }\to \mathbf
Complex_projective_space
Branch of mathematics
considerable interest in physics. The apparatus of vector bundles, principal bundles, and connections on bundles plays an extraordinarily important role in modern
Differential_geometry
Hypothetical particle with one magnetic pole
over a principal G-bundle over spacetime. G is the gauge group, and it acts on each fiber of the bundle separately. A connection on a G-bundle tells you
Magnetic_monopole
Type of group in mathematics
clutching construction, homotopy groups of the stable space O are identified with stable vector bundles on spheres (up to isomorphism), with a dimension
Orthogonal_group
Mathematics textbook
with complex geometry, which includes Kähler manifolds and (stable) holomorphic vector bundles. Simon Donaldson and Peter Kronheimer both obtained their
The Geometry of Four-Manifolds
The_Geometry_of_Four-Manifolds
Application of topology
connected. The tangent bundle T X {\displaystyle TX} of a world manifold X {\displaystyle X} and the associated principal frame bundle F X {\displaystyle
World_manifold
Mathematical object studied in the field of algebraic geometry
d)} of isomorphism classes of stable vector bundles of rank n and degree d as an open subset. Since a line bundle is stable, such a moduli is a generalization
Algebraic_variety
Algorithmic technique using hashing
Algorithm based on p-stable Random Projection TLSH open source on Github JavaScript port of TLSH (Trend Micro Locality Sensitive Hashing) bundled as node.js module
Locality-sensitive_hashing
Video game series
in 2001 by FastTrak Software Publishing as Creatures Internet Edition, a bundle of Creatures 3, Creatures 3 Update 2, Docking Station, and a number of environment
Creatures_(video_game_series)
Theorem in homotopy theory
the structure of a CW-complex, one may consider the category of principal G-bundles. One can define a functor from the category of CW-complexes to the
Segal's_conjecture
Array of numbers
conjugate gradient method. An algorithm is, roughly speaking, numerically stable if little deviations in the input values do not lead to big deviations in
Matrix_(mathematics)
Set in game theory
coalition having at least (n+1)/2 members has an empty core. That is, no stable coalition exists. Consider a group of n miners, who have discovered large
Core_(game_theory)
Branch of geometry
structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a condition called 'complete non-integrability'. Equivalently
Contact_geometry
an honorary member. Mike meets Tom and becomes a clumsy, accident-prone bundle of nerves. Tom becomes the recipient of a series of messy but funny indignities
List of My Three Sons episodes
List_of_My_Three_Sons_episodes
Identity management system
macOS, and other Unix-based clients. As of September 2026, the current stable release is FreeIPA 4.13.4, issued to fix two security vulnerabilities, one
FreeIPA
quasi-coherent sheaves on it. See also https://mathoverflow.net/q/16257 G-bundle A principal G-bundle. generic point A dense point. genus See #arithmetic genus, #geometric
Glossary of algebraic geometry
Glossary_of_algebraic_geometry
Prime Minister of Israel (1996–1999; 2009–2021; 2022–present)
Italian-American woman.[relevant?] Netanyahu has been suffering from right bundle branch block (RBBB) since around 2003. In the first half of 2008, doctors
Benjamin_Netanyahu
or in other words, the O ( d ) {\displaystyle {\mathcal {O}}(d)} -principal bundle associated to T M {\displaystyle TM} . Let W {\displaystyle W} be an
Stochastic analysis on manifolds
Stochastic_analysis_on_manifolds
Line of smartwatches
dongle plugged into the headphone jack. Early on, the user interface and bundled apps were inspired by the iPhone, but they were too complex and underwent
Apple_Watch
Province of Canada
measure of a "metro area", the Census Metropolitan Area (CMA), roughly bundles together population figures from the core municipality with those from
Ontario
Chinese classic text
the latter half of the Warring States period (475 – 221 BCE). Though its bundles are unlikely as a unified text, they are nominally taken as a version from
Tao_Te_Ching
1977 film by David Lynch
Henry's one-room apartment and begins caring for the child, a swaddled bundle with an inhuman face that resembles the spermatozoon creature seen earlier
Eraserhead
Scottish philosopher, historian, economist and essayist (1711–1776)
positing that they experience only a bundle of sensations and that the self is nothing more than this bundle of perceptions connected by an association
David_Hume
Open-source server virtualization platform
subscription licensing and consolidated many products into a smaller number of bundled offerings. The free edition of VMware's vSphere Hypervisor, commonly known
Proxmox_Virtual_Environment
Dutch philosopher and theologian (c. 1466–1536)
several edifying essays on methodology, then a highly revised Vulgate—all bundled as his Novum testamentum omne and pirated individually throughout Europe—
Erasmus
List of versions of the Java programming language
September 2025. The first version was released on January 23, 1996. The first stable version, JDK 1.0.2, is called Java 1. It included: core language features
Java_version_history
Actin-binding protein
kDa tissue-specific actin-binding protein associated with the actin core bundle of the brush border. Villin-1 is encoded by the VIL1 gene. Villin-1 contains
Villin-1
South Korean television series (2021–2025)
Giant Swing. Call of Duty teamed up with Squid Game to create a special bundle, with Tom Choi reprising his role as the masked voice of the Front Man.
Squid_Game
Free compiler and IDE for Pascal and ObjectPascal
0.x releases, the port to 68k CPU was redone, and the compiler produced stable code for several 68k Unix-like and AmigaOS operating systems. During the
Free_Pascal
Concept in mathematics
{\displaystyle \mathbb {HP} ^{1}=S^{4}} , its tangent bundle is stably trivial. The tangent bundles of the rest have nontrivial Stiefel–Whitney and Pontryagin
Quaternionic_projective_space
Film by Timur Bekmambetov
Baby' Tops Overseas Again As 'Magnificent 7' Corrals $19.2M & 'Storks' Bundles $18.3M – Intl Box Office". Deadline Hollywood. Archived from the original
Ben-Hur_(2016_film)
Open source automation server
as Apache Tomcat, or by default as a stand-alone web-application in co-bundled Eclipse Jetty. It supports version control tools, including AccuRev, CVS
Jenkins_(software)
Tamil-vocabulary programming language for finance
and a Visual Studio Code extension that bundles the full toolchain. Versions 1.0.1 to 1.0.3 added a bundled typeface released under the SIL Open Font
ETamil
Central banking system of the US
influencing market interest rates to achieve the goals of Maximum employment Stable prices, interpreted as an inflation rate of 2 percent per year on average
Federal_Reserve
(January 11, 2023). "Baby Ruby Trailer – Magnet Horror Movie Delivers a Bundle of Nightmares in February". Bloody Disgusting. Archived from the original
List of American films of 2023
List_of_American_films_of_2023
Allotropes of carbon with a cylindrical nanostructure
conducting yarn. The electronic properties of individual CNT fibers (i.e. bundle of individual CNT) are governed by the two-dimensional structure of CNTs
Carbon_nanotube
American short-range air-to-air missile
battery with a turbo-alternator. The AIM-9H also included a continuous-rod bundle warhead, improving its destructive capability. The AIM-9H was the last and
AIM-9_Sidewinder
Atomic model introduced by Niels Bohr in 1913
symplectic form should be the curvature form of a connection of a Hermitian line bundle, which is called a prequantization. Bohr also updated his model in 1922
Bohr_model
Messaging and VoIP service owned by Meta
messaging service, maybe search and other things like weather. Providing a bundle of these free of charge to users will work like a gateway drug of sorts
Locations where civilization emerged
remodeled, with major burnt offerings associated with the remodeling. Bundles of strings uncovered at Norte Chico sites have been identified as quipu
Cradle_of_civilization
Locally spherical point on a mathematical surface
all directions are equal, hence, both principal curvatures are equal, and every tangent vector is a principal direction. The name "umbilic" comes from
Umbilical_point
of their cytoplasmic signaling domain. HAMP domains comprise four-helix bundle signaling elements that mediate input-output transactions in many microbial
John_S._Parkinson
appearance given by the coordinated beat pattern of the anterior flagellar bundle of Cthulhu cells is reminiscent of this demon" Cthylla microfasciculumque
List of organisms named after works of fiction
List_of_organisms_named_after_works_of_fiction
Linux-based operating system developed by Google
derived from Gentoo Linux), and uses the Google Chrome web browser as its principal user interface. Google announced the project in July 2009, initially describing
ChromeOS
Violent tactic resulting in the attacker's intentional death
Japanese tanks in one incident obliterating four Japanese tanks with grenade bundles. During the 1946–1950 Communist Revolution, coolies, poor laborers, fighting
Suicide_attack
Bridge in New York City
cylindrical shape. These wires are bundled in 19 individual strands, with 278 wires to a strand. This was the first use of bundling in a suspension bridge and
Brooklyn_Bridge
American film and distribution company
(1982), p. 168. "RKO General Wants 'Warranties' Before Buying NTA's Post-'48 Bundle". Variety. August 24, 1960. p. 36. Retrieved May 14, 2023. "Papers Read
RKO_Pictures
Gradient flow of the Yang–Mills action functional
{g}}} and E ↠ B {\displaystyle E\twoheadrightarrow B} be a principal G {\displaystyle G} -bundle with a compact orientable Riemannian manifold B {\displaystyle
Yang–Mills_flow
Family of text editors
Software. Versions for DOS, Windows, Linux, FreeBSD, Mac OS X and OS/2 are bundled in the release. It uses a non-Lisp extension language with C syntax and
Emacs
Prime Minister of Japan (2006–2007; 2012–2020)
that The Economist described as "less a single arrow than a 1,000-strong bundle" and compared favorably to the 2013 announcement. These new measures included
Shinzo_Abe
Japanese mathematician
as it implies semistability and decomposability as a direct sum of stable bundles. This establishes one direction of the Kobayashi–Hitchin correspondence
Shoshichi_Kobayashi
American electric vehicle and clean energy company
because each has a relatively low capacity, so thousands needed to be bundled together in a battery pack. Electrical and thermal management also proved
Tesla,_Inc.
Raster graphics editing software
was changed to that of subscription model. Historically, Photoshop was bundled with additional software such as Adobe ImageReady, Adobe Fireworks, Adobe
Adobe_Photoshop
Biological process to convert light into chemical energy
malate synthesized by this process is then translocated to specialized bundle sheath cells where the enzyme RuBisCO and other Calvin cycle enzymes are
Photosynthesis
Sale of goods and services
include discounts, everyday low pricing, high–low pricing, loss leaders, bundling, and psychological pricing, alongside planning for customer payment modes
Retail
2007 mortgage crisis in the United States
failure froze short-term funding for big firms." Securitization – the bundling of bank loans to create tradeable bonds – started in the mortgage industry
Subprime_mortgage_crisis
First planet from the Sun
extremely "leaky". The spacecraft encountered magnetic "tornadoes"—twisted bundles of magnetic fields connecting the planetary magnetic field to interplanetary
Mercury_(planet)
Relativistic quantum mechanical wave equation
μ a {\displaystyle A_{\mu }^{a}} , formally the connection on the principal bundle, which necessarily transforms in the adjoint representation of the
Dirac_equation
Protection from financial loss
about 1300 AD. Separate insurance contracts (i.e., insurance policies not bundled with loans or other kinds of contracts) were invented in Genoa in the 14th
Insurance
Branch of mathematics
it comes with a unique path lifting. If E {\displaystyle E} is a principal G-bundle over a paracompact space, that is, a space with a free and transitive
Homotopy_theory
Cooperation between firms to limit competition
themselves Tying agreements and anticompetitive Product bundling (although, not all product bundling is anticompetitive) Refusal to deal with certain customers
Collusion
Cultural and artistic movement
ontological claim (that the self just is the bundle) or an epistemological claim (we only know of the self as a bundle). Hume's scepticism about the self underlies
Modernism
Central nervous system stimulant
Secondly, around the vascular bundles, where it probably inhibits pathogenic fungi from entering and colonizing the vascular bundles. Caffeine in nectar may
Caffeine
American investment bank
Times. Morgenson, Gretchen; Story, Louise (December 23, 2009). "Banks Bundled Bad Debt, Bet Against It and Won". The New York Times. Archived from the
Goldman_Sachs
brush-like bundle of needles) set perpendicular to a wooden handle in an L-shape (hence "hafted"). This handle makes the needle more stable and easier
History_of_tattooing
Power generated from nuclear reactions
limit radiation exposure. After being removed from the reactors, used fuel bundles are stored for six to ten years in spent fuel pools, which provide cooling
Nuclear_power
Social science studying goods and services
approach he favoured as "combin[ing the] assumptions of maximizing behaviour, stable preferences, and market equilibrium, used relentlessly and unflinchingly
Economics
American multinational technology company
developing its own Apple silicon processors, the macOS operating system, and bundled applications including Safari, iMovie, GarageBand, and the iWork productivity
Apple_Inc.
Free and open-source chess engine
default chess engine bundled with the Internet Chess Club interface programs BlitzIn and Dasher. On mobile, it has been bundled with the Stockfish app
Stockfish_(chess)
Death of a region of brain cells due to poor blood flow
Chen X, Ouyang M, Billot L, et al. (July 2023). "The third Intensive Care Bundle with Blood Pressure Reduction in Acute Cerebral Haemorrhage Trial (INTERACT3):
Stroke
Electronic musical instrument
Deutsch, Richard Teitelbaum, Vladimir Ussachevsky and Wendy Carlos. Moog's principal innovation was voltage control, which uses voltage to control pitch. He
Moog_synthesizer
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STABLE PRINCIPAL-BUNDLE
STABLE PRINCIPAL-BUNDLE
Female
English
Elaborated form of English Star, STARLA means "star."
Boy/Male
Tamil
Siddhanth Nair | ஸிதà¯à®¤à®¾à®‚த நீர
Principal
Siddhanth Nair | ஸிதà¯à®¤à®¾à®‚த நீர
Female
English
Feminine variant spelling of English unisex Stacey, STACIE means "resurrection."
Female
English
Feminine variant spelling of English unisex Stacey, STACEE means "resurrection."
Female
English
Variant spelling of English Mabel, MABLE means "lovable."Â
Surname or Lastname
English
English : from Middle English stapel ‘post’, hence a topographic name for someone who lived near a boundary post, or a habitational name from some place named with this word (Old English stapel), as for example Staple in Kent or Staple Fitzpaine in Somerset.Americanized spelling of German Stapel.
Male
French
French name derived from Latin amabilis, AMABLE means "lovable."
Boy/Male
Indian, Punjabi, Sikh
Stable
Surname or Lastname
English (Devon and Cornwall)
English (Devon and Cornwall) : habitational name from Scoble in Devon.
Surname or Lastname
English
English : occupational name for someone who looked after horses or cattle, from an agent derivative of Middle English stable ‘stable’.German (Stäbler) : occupational name for an official who carried a staff as a symbol of office, Middle High German stebelære.
Surname or Lastname
English
English : variant of Staple.
Boy/Male
Indian, Sanskrit
Stable
Surname or Lastname
English, Dutch, North German, and Danish
English, Dutch, North German, and Danish : variant of Stubbe.
Surname or Lastname
English
English : topographic name for someone who lived by a stable, or an occupational name for someone employed in one, from Middle English stable, plural stables (via Old French from Latin stabulum, a derivative of stare ‘to stand’). In Middle English the term was used of the quarters occupied by cattle as well as those reserved for horses.
Boy/Male
Hindu
Principal
Boy/Male
Tamil
Stable
Boy/Male
Vietnamese
Stable.
Boy/Male
Hindu
Stable
Boy/Male
Shakespearean American English
Henry VI, Part 2' Sir John Stanley. 'King Henry the Sixth, Part III' Sir William Stanley. 'King...
Female
English
English name derived from the vocabulary word, SABLE means "black," as a heraldic color. It is sometimes confused with the mammal of the same name but which has brown fur, not black, and which has a different origin.
STABLE PRINCIPAL-BUNDLE
STABLE PRINCIPAL-BUNDLE
STABLE PRINCIPAL-BUNDLE
STABLE PRINCIPAL-BUNDLE
STABLE PRINCIPAL-BUNDLE
STABLE PRINCIPAL-BUNDLE
STABLE PRINCIPAL-BUNDLE
n.
The principal commodity of traffic in a market; a principal commodity or production of a country or district; as, wheat, maize, and cotton are great staples of the United States.
v. i.
A house, shed, or building, for beasts to lodge and feed in; esp., a building or apartment with stalls, for horses; as, a horse stable; a cow stable.
v. t.
To put or keep in a stable.
adv.
In a principal manner; primarily; above all; chiefly; mainly.
v. i.
Firmly established; not easily moved, shaken, or overthrown; fixed; as, a stable government.
imp. & p. p.
of Stable
a.
Being of reasonable or suitable size; as, sizable timber; sizable bulk.
n.
The fiber of wool, cotton, flax, or the like; as, a coarse staple; a fine staple; a long or short staple.
v. i.
Durable; not subject to overthrow or change; firm; as, a stable foundation; a stable position.
adv.
In a stable manner; firmly; fixedly; steadily; as, a government stably settled.
v. t.
To sort according to its staple; as, to staple cotton.
a.
Not stable; not standing fast or firm; unstable; prone to change or recede from a purpose; mutable; inconstant.
n.
The principal constituent in anything; chief item.
a.
Pertaining to, or being market of staple for, commodities; as, a staple town.
n.
A principal or essential point or rule; a principle.
n.
A view of the contents of a work; a statement of the principal topics discussed; an index; a syllabus; a synopsis; as, a table of contents.
v. i.
To dwell or lodge in a stable; to dwell in an inclosed place; to kennel.
n.
A stable keeper.
a.
Liable to, or subjected by law to, taxation; as, ratable estate.
a.
Highest in rank, authority, character, importance, or degree; most considerable or important; chief; main; as, the principal officers of a Government; the principal men of a state; the principal productions of a country; the principal arguments in a case.
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