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English pastoralist and politician
Peter Manifold (1817–1885) was an English pastoralist and politician of western Victoria. Born in 1817 to William and Mary Manifold in Bromborough, Cheshire
Peter_Manifold
Topics referred to by the same term
geometry. Manifold may also refer to: Manifold (comics), a fictional character in Marvel Comics publications Manifold Records, a record label Manifold Trilogy
Manifold_(disambiguation)
Suburb of Geelong, Victoria, Australia
District pastoralists, John and Peter Manifold. The Post Office opened on 25 March 1929, but has always been known as Manifold. Holy Spirit Church, located
Manifold_Heights
Smooth manifold with an inner product on each tangent space
In differential geometry, a Riemannian manifold (or Riemann space) is a geometric space on which many geometric notions such as distance, angles, length
Riemannian_manifold
Mathematical space
In mathematics, a 3-manifold is a topological space that locally looks like a three-dimensional Euclidean space. A 3-manifold can be thought of as a possible
3-manifold
Subclass of manifold
In mathematics, a spherical 3-manifold M is a 3-manifold of the form M = S 3 / Γ {\displaystyle M=S^{3}/\Gamma } where Γ {\displaystyle \Gamma } is a finite
Spherical_3-manifold
Mathematical space
In mathematics, a 4-manifold is a 4-dimensional topological manifold. A smooth 4-manifold is a 4-manifold with a smooth structure. In dimension four,
4-manifold
Mathematics textbook
field, and Peter Kronheimer. It was published on 13 September 1990 with a second revised edition in 1997. The Geometry of Four-Manifolds first describes
The Geometry of Four-Manifolds
The_Geometry_of_Four-Manifolds
Historic homestead in Victoria, Australia
Brothers Peter and John Manifold travelled with their parents, William and Mary, and three sisters to join their elder brother Thomas Manifold, who had
Purrumbete
Mathematical concept
of a center manifold was originally developed to determine stability of degenerate equilibria. Subsequently, the concept of center manifolds was realised
Center_manifold
Smallest closed orientable hyperbolic 3-manifold
Meyerhoff, and Peter Milley (2009) showed that it has the smallest volume of any closed orientable hyperbolic 3-manifold. The manifold was independently
Weeks_manifold
Symplectic topology tool
infinite-dimensional manifold and a real valued function on it. In the symplectic version, this is the free loop space of a symplectic manifold with the symplectic
Floer_homology
Australian politician (1809–1875)
Legislative Assembly. Manifold was born on 29 March 1809 in Bromborough, England. He was the son of William Manifold and Mary Manifold (née Barnes). He had
Thomas_Manifold
Hadamard manifold, named after Jacques Hadamard — more often called a Cartan–Hadamard manifold, after Élie Cartan — is a Riemannian manifold ( M , g )
Hadamard_manifold
Topological space
A Seifert fiber space is a 3-manifold together with a decomposition as a disjoint union of circles. In other words, it is a S 1 {\displaystyle S^{1}} -bundle
Seifert_fiber_space
Town in Victoria, Australia
gatherer society. The first British settlers, the Manifold brothers (Thomas, John and Peter Manifold), arrived in the area from Van Diemen's Land (Tasmania)
Camperdown,_Victoria
Historic homestead in Victoria, Australia
Boortkoi (sold to Peter Manifold of Purrumbete), Berrambool, Salt Creek (leased to Peter McIntyre) and Flat Top Hill (leased to Peter Armstrong). Berrambool
Berrambool
American mathematician
geometrization conjecture. Li, Peter; Yau, Shing Tung (1980). "Estimates of eigenvalues of a compact Riemannian manifold". In Osserman, Robert; Weinstein
Peter_Li_(mathematician)
In mathematics, a smooth compact manifold M is called almost flat if for any ε > 0 {\displaystyle \varepsilon >0} there is a Riemannian metric g ε {\displaystyle
Almost_flat_manifold
Mathematics timeline
timeline of manifolds, one of the major geometric concepts of mathematics. For further background see history of manifolds and varieties. Manifolds in contemporary
Timeline_of_manifolds
Mathematics concept
In mathematics, a Haken manifold is a compact, P²-irreducible 3-manifold that is sufficiently large, meaning that it contains a properly embedded two-sided
Haken_manifold
Concept in differential geometry
In differential geometry, in the category of differentiable manifolds, a fibered manifold is a surjective submersion π : E → B {\displaystyle \pi :E\to
Fibered_manifold
particular instances of arithmetic groups. An arithmetic hyperbolic three-manifold is the quotient of hyperbolic space H 3 {\displaystyle \mathbb {H} ^{3}}
Arithmetic hyperbolic 3-manifold
Arithmetic_hyperbolic_3-manifold
American mathematician
Shalen, Peter B. (1979). Seifert fibered spaces in 3-manifolds. Providence: American Mathematical Society. ISBN 0-8218-2220-9. Shalen, Peter B. Separating
Peter_Shalen
mathematics, the slow manifold of an equilibrium point of a dynamical system occurs as the most common example of a center manifold. One of the main methods
Slow_manifold
Comics character
Eden Fesi, also known as Manifold, is a superhero appearing in American comic books published by Marvel Comics. Created by Jonathan Hickman and Stefano
Eden_Fesi
Branch of differential geometry
branch of differential geometry that studies Riemannian manifolds. An example of a Riemannian manifold is a surface, on which distances are measured by the
Riemannian_geometry
Process in mathematics of decomposing a topological space
Geometrization conjecture Manifold decomposition Satellite knot Jaco, William H.; Shalen, Peter B (1979), "Seifert fibered spaces in 3-manifolds", Memoirs of the
JSJ_decomposition
British mathematician
385. Freedman, Michael; Hass, Joel; Scott, Peter (1983). "Least area incompressible surfaces in 3-manifolds". Inventiones Mathematicae. 71 (3): 609–642
G._Peter_Scott
American mathematician
2004.159.1027. S2CID 119143219. Ozsváth, Peter; Szabó, Zoltán (2004). "Holomorphic disks and three-manifold invariants: properties and applications".
Peter_Ozsváth
Manifold that "locally looks like" Euclidean space
mathematics, a Riemannian manifold is said to be flat if its Riemann curvature tensor is everywhere zero. Intuitively, a flat manifold is one that "locally
Flat_manifold
Constant in Riemannian geometry
Riemannian geometry, the Cheeger isoperimetric constant of a compact Riemannian manifold M is a positive real number h(M) defined in terms of the minimal area of
Cheeger_constant
In geometry, a tame manifold is a manifold with a well-behaved compactification. More precisely, a manifold M {\displaystyle M} is called tame if it is
Tame_manifold
Partial differential equation
use of a technique pioneered by Peter Li and Shing-Tung Yau for parabolic differential equations on Riemannian manifolds, Hamilton (1993a) proved the following
Ricci_flow
Branch of mathematics
manifolds. A manifold is a topological space that resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has
Topology
British army officer and Aboriginal Protector
as a station manager for two Western District squatters, Charles and Peter Manifold, before he died in 1851 after falling from a horse near Mt Leura, His
Charles_Sievwright
Three dimensional analogue of uniformization conjecture
space. Instead, the geometrization conjecture states that every closed 3-manifold can be decomposed in a canonical way into pieces that each have one of
Geometrization_conjecture
definitions given below. Connection Curvature Metric space Riemannian manifold See also: Glossary of general topology Glossary of differential geometry
Glossary of Riemannian and metric geometry
Glossary_of_Riemannian_and_metric_geometry
Russian-French mathematician
careful exposition by Peter Buser and Hermann Karcher. In 1979, Richard Schoen and Shing-Tung Yau showed that the class of smooth manifolds which admit Riemannian
Mikhael Gromov (mathematician)
Mikhael_Gromov_(mathematician)
Irish businessman (born 1953)
until his retirement on 1 January 2014, when he was succeeded by Albert Manifold. CRH is Ireland's largest company; its primary listing is on the London
Myles_Lee
Generalization of Riemannian manifolds
mathematics, particularly differential geometry, a Finsler manifold is a differentiable manifold M where a (possibly asymmetric) Minkowski norm F(x, −) is
Finsler_manifold
Topological space in mathematics
non-paracompact manifolds in higher dimensions include the Prüfer manifold, products of any non-paracompact manifold with any non-empty manifold, the ball of
Long_line_(topology)
Set of points where the shortest paths from a specific starting point cease to be unique
geometry, the cut locus of a point p on a manifold is the closure of the set of all other points on the manifold that are connected to p by two or more distinct
Cut_locus
mathematics, a Riemannian submersion is a submersion from one Riemannian manifold to another that respects the metrics, meaning that it is an orthogonal
Riemannian_submersion
Description in Riemannian geometry
curvature is one of the ways to describe the curvature of Riemannian manifolds. The sectional curvature K ( σ p ) {\displaystyle K(\sigma _{p})} depends
Sectional_curvature
Study in mathematical gauge theory
4310/jdg/1214437665, MR 0710056. Donaldson, Simon K.; Kronheimer, Peter B. (1990-09-13). The Geometry of Four-Manifolds. Oxford Mathematical Monographs. Oxford University
Donaldson_theory
Country in West Asia
like Kilim, Soumak, and embroidered tissues like Suzani are part of the manifold tradition of Persian carpet weaving. Iran produces three-quarters of the
Iran
On the finite presentability of fundamental groups of 3-manifolds
fundamental groups of 3-manifolds due to G. Peter Scott, (Scott 1973). The precise statement is as follows: Given a 3-manifold (not necessarily compact)
Scott_core_theorem
Historic homestead in Victoria, Australia
pastoralist Peter McArthur. After arriving in Melbourne and travelling to the fledgling settlement of Geelong, the pair purchased sheep from Peter Manifold at
West_Cloven_Hills
Russian mathematician (born 1966)
solutions of the Ricci flow on three-manifolds". Comm. Anal. Geom. 7 (4): 695–729. doi:10.4310/CAG.1999.v7.n4.a2. Li, Peter; Yau, Shing-Tung (1986). "On the
Grigori_Perelman
American mathematician (1943–2024)
required the stronger assumption that the underlying closed Riemannian manifold has nonnegative sectional curvature and parallel Ricci tensor (such as
Richard_S._Hamilton
Chinese-American mathematician (born 1949)
functions on a Riemannian manifold, although Yau and Cheng−Yau's original results cover more general scenarios. In 1986, Yau and Peter Li made use of the same
Shing-Tung_Yau
Normalized hyperbolic volume of the complement of a hyperbolic knot
of Three-Manifolds, p. 165, archived from the original (PDF) on 2020-07-27, retrieved 2020-10-19 Gabai, David; Meyerhoff, Robert; Milley, Peter (2009),
Hyperbolic_volume
Generalized manifold
the word "manifold" already has a different definition. I tried "foldamani", which was quickly displaced by the suggestion of "manifolded". After two
Orbifold
hyperbolic 3-manifold with finitely generated fundamental group is topologically tame, in other words homeomorphic to the interior of a compact 3-manifold. The
Tameness_theorem
manifolds". Annals of Global Analysis and Geometry. 9 (2): 129–143. doi:10.1007/BF00776852. ISSN 0232-704X. Kolář, Ivan; Slovák, Jan; Michor, Peter W
Natural_bundle
Branch of geometry
mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a
Contact_geometry
British mathematician (born 1945)
Cambridge University Press, 1997. Eccles, Peter John. "Multiple points of codimension one immersions of oriented manifolds." Mathematical Proceedings of the Cambridge
Peter_Eccles_(mathematician)
Isomorphism of differentiable manifolds
is an isomorphism of differentiable manifolds. It is an invertible function that maps one differentiable manifold to another such that both the function
Diffeomorphism
Former railway line in Staffordshire, England
The Leek and Manifold Valley Light Railway (L&MVLR) was a narrow gauge railway in Staffordshire, England, that operated between 1904 and 1934. The line
Leek and Manifold Valley Light Railway
Leek_and_Manifold_Valley_Light_Railway
Invariant of a quadratic form over a field of characteristic 2
invariant of (4k + 2)-dimensional manifolds (singly even-dimensional manifolds: surfaces (2-manifolds), 6-manifolds, 10-manifolds, etc.) with certain additional
Arf_invariant
Assignment of vector fields to manifolds
In mathematics, the tangent space of a manifold is a generalization of tangent lines to curves in two-dimensional space and tangent planes to surfaces
Tangent_space
Concept in topology
oriented manifolds of the same dimension is a number that represents the number of times that the domain manifold wraps around the range manifold under the
Degree of a continuous mapping
Degree_of_a_continuous_mapping
Mathematical manifold theory
D. Hodge, is a method for studying the cohomology groups of a smooth manifold M using partial differential equations. The key observation is that, given
Hodge_theory
Decomposition of a compact oriented 3-manifold by dividing it into two handlebodies
splitting (Danish: [ˈhe̝ˀˌkɒˀ] ) is a decomposition of a compact oriented 3-manifold that results from dividing it into two handlebodies. Let V and W be handlebodies
Heegaard_splitting
Operation on fibered manifolds
differential geometry, a fibered manifold is surjective submersion of smooth manifolds Y → X. Locally trivial fibered manifolds are fiber bundles. Therefore
Connection_(fibred_manifold)
Romanian-American mathematician
Sciences in 2021. Constantin, Peter; Foias, Ciprian; Temam, Roger; Nicolaenko, B. (1988). Integral manifolds and inertial manifolds for dissipative partial
Peter_Constantin
Differentiable function whose derivative is everywhere injective
mathematics, an immersion is a differentiable function between differentiable manifolds whose differential pushforward is everywhere injective. Explicitly, f :
Immersion_(mathematics)
Compact astronomical body
doi:10.3847/1538-4357/abc6aa. ISSN 0004-637X. Kaczmarek, Zofia; McGill, Peter; Perkins, Scott E.; Dawson, William A.; Huston, Macy; Ho, Ming-Feng; Abrams
Black_hole
Scuba component used to functionally connect diving cylinders
A scuba manifold is a device incorporating one or more valves and one or more gas outlets with scuba regulator connections, used to connect two or more
Scuba_manifold
Restricts the possible topology of a negatively curved compact Riemannian manifold
curved compact Riemannian manifold. It is named for Alexandre Preissmann, who published a proof in 1943. Consider a closed manifold with a Riemannian metric
Preissmann's_theorem
Continuous surjection satisfying a local triviality condition
category of smooth manifolds. That is, E {\displaystyle E} , B {\displaystyle B} , and F {\displaystyle F} are required to be smooth manifolds and all the functions
Fiber_bundle
On when a definite intersection form of a smooth 4-manifold is diagonalizable
states that a definite intersection form of a closed, oriented, smooth manifold of dimension 4 is diagonalizable. If the intersection form is positive
Donaldson's_theorem
British mathematician (born 1963)
2020. Taubes, Clifford Henry (2009). "Review: Monopoles and three-manifolds by Peter Kronheimer and Tomasz Mrowka" (PDF). Bull. Amer. Math. Soc. (N.S.)
Peter_B._Kronheimer
I-bundle is a fiber bundle whose fiber is an interval and whose base is a manifold. Any kind of interval, open, closed, semi-open, semi-closed, open-bounded
I-bundle
Mathematics award
Retrieved 21 February 2026. Nasar, Sylvia; Gruber, David (21 August 2006). "Manifold Destiny: A legendary problem and the battle over who solved it". The New
Fields_Medal
Theory of subatomic structure
compact extra dimensions must be shaped like a Calabi–Yau manifold. A Calabi–Yau manifold is a special space which is typically taken to be six-dimensional
String_theory
Dutch-American computer scientist
Open Source Convention, (InterMezzo) Braam, Peter J. (1987). Magnetic Monopoles and Hyperbolic Three-manifolds. University of Oxford. Retrieved March 19
Peter_Braam
Poem by J. S. Manifold
The Tomb of Lt. John Learmonth, AIF is a poem by Australian poet J. S. Manifold. It was first published in New Republic magazine on 10 September 1945,
The Tomb of Lt. John Learmonth, AIF
The_Tomb_of_Lt._John_Learmonth,_AIF
Australian conservationist (1962–2006)
Bailout bottle Decompression cylinder Independent doubles Manifolded twin set Scuba manifold Pony bottle Scuba configuration Sidemount Sling cylinder Diving
Steve_Irwin
Field of mathematical analysis
also called analysis on manifolds, is the study of the global and topological properties of differential equations on manifolds and vector bundles. Global
Global_analysis
Form of differential geometry
invariants of manifolds and polyhedra, as initially conceived by Charles Loewner and developed by Mikhail Gromov, Michael Freedman, Peter Sarnak, Mikhail
Systolic_geometry
German mathematician (1927–2012)
Ernst Peter Hirzebruch ForMemRS (17 October 1927 – 27 May 2012) was a German mathematician, working in the fields of topology, complex manifolds and algebraic
Friedrich_Hirzebruch
American mathematician
theory, low dimensional topology, 3-manifolds, and hyperbolic geometry. Culler frequently collaborates with Peter Shalen and they have co-authored many
Marc_Culler
topological theory based on the concept of the boundary of a manifold. For context see timeline of manifolds. Jean Dieudonné wrote that cobordism returns to the
Timeline_of_bordism
American mathematician (born 1938)
1016/0040-9383(70)90061-3. with Frank Raymond: Orlik, Peter; Raymond, Frank (1970). "Actions of the torus on 4-manifolds. I". Transactions of the American Mathematical
Peter_Orlik
Italian shark diver and conservationist
Bailout bottle Decompression cylinder Independent doubles Manifolded twin set Scuba manifold Pony bottle Scuba configuration Sidemount Sling cylinder Diving
Cristina_Zenato
Whether a manifold which is a homotopy sphere is a sphere
conjecture is a statement that a manifold that is a homotopy sphere is a sphere. More precisely, one fixes a category of manifolds: topological (Top), piecewise
Generalized Poincaré conjecture
Generalized_Poincaré_conjecture
Historic homestead in Victoria, Australia
extensive Purrumbete pastoral run established by brothers John, Peter and Thomas Manifold, who became the first European settlers in the Camperdown district
Talindert
Theorem stating that smooth algebraic curve has minimum genus its homology class
as proved for example by Peter Ozsváth and Szabó in 2000). It states that a symplectic surface of a symplectic 4-manifold is genus minimizing within
Thom_conjecture
List of all members of the avengers
Cannonball Samuel "Sam" Zachary Guthrie Captain Universe Tamara Devoux Manifold Eden Fesi Smasher Isabel "Izzy" Kane Sunspot Roberto "Bobby" da Costa Zheng
List_of_Avengers_members
Measure of difference between two points
information geometry the corresponding statistical manifold is interpreted as a (dually) flat manifold. This allows many techniques of optimization theory
Bregman_divergence
Independent aerospace manufacturer and defense contractor
the engine to force air into the combustion process through the intake manifold. The exhaust based turbocharger most common today was first created for
Honeywell_Aerospace
German mathematician
classification of 4-manifolds. Together with the Fields medalist Mike Freedman, Peter Teichner made contributions to the classification of 4-manifolds whose fundamental
Peter_Teichner
When a closed manifold embedded in M has an isotopy onto a boundary component of M
In mathematics, a connected submanifold of a compact manifold with boundary is said to be boundary parallel, ∂-parallel, or peripheral if it can be continuously
Boundary_parallel
times and in all circumstances, wholly freed from restraint. There are manifold restraints to which every person is necessarily subject for the common
Anti-vaccine_activism
invariants of the smooth structure of four-dimensional smooth manifolds (short 4-manifolds) based on the methods behind Donaldson's theorem. In particular
Donaldson_invariant
Linear operators with a common spectrum
analogous equations, by Peter Lax, showed how linear machinery could explain the non-linear behaviour. Two closed Riemannian manifolds are said to be isospectral
Isospectral
Isometry group of a compact Riemannian manifold with negative Ricci curvature is finite
of a compact Riemannian manifold with negative Ricci curvature must be zero. Consequently the isometry group of the manifold must be finite. The theorem
Bochner's theorem (Riemannian geometry)
Bochner's_theorem_(Riemannian_geometry)
Hungarian mathematician
University in 1994. Together with Peter Ozsváth, Szabó created Heegaard Floer homology, a homology theory for 3-manifolds. For this contribution to the field
Zoltán_Szabó_(mathematician)
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