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Bundle in which the fiber is a surface
In mathematics, a surface bundle is a bundle in which the fiber is a surface. When the base space is a circle the total space is three-dimensional and
Surface_bundle
In mathematics, a surface bundle over the circle is a fiber bundle with base space a circle, and with fiber space a surface. Therefore the total space
Surface bundle over the circle
Surface_bundle_over_the_circle
Topological space
a , b ) {\displaystyle (a,b)} with a > 0 {\displaystyle a>0} is the surface bundle of the automorphism of a disk given by rotation by an angle of 2 π b
Seifert_fiber_space
Transport system component in vascular plants
mesophyll cells lie between the bundle sheath and the leaf surface. The Calvin cycle is confined to the chloroplasts of these bundle sheath cells in C4 plants
Vascular_bundle
A torus bundle, in the sub-field of geometric topology in mathematics, is a kind of surface bundle over the circle, which in turn is a class of three-manifolds
Torus_bundle
Collection of heart muscle cells
The bundle of His (BH) or His bundle (HB) (/hɪs/ "hiss") is a collection of heart muscle cells specialized for electrical conduction. As part of the electrical
Bundle_of_His
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
Possibility of a consistent definition of "clockwise" in a mathematical space
also be expressed in terms of the tangent bundle. The tangent bundle is a vector bundle, so it is a fiber bundle with structure group GL ( n , R ) {\displaystyle
Orientability
Concept in algebraic geometry
canonical bundle of a non-singular algebraic variety V {\displaystyle V} of dimension n {\displaystyle n} over a field is the line bundle Ω n = ω {\displaystyle
Canonical_bundle
Type of vector bundle
'Higgs bundle', and the condition φ ∧ φ = 0 {\displaystyle \varphi \wedge \varphi =0} (which is vacuous in Hitchin's original set-up on Riemann surfaces) was
Higgs_bundle
Quillen determinant line bundle is a line bundle over the space of Cauchy–Riemann operators of a vector bundle over a Riemann surface, introduced by Quillen (1985)
Quillen determinant line bundle
Quillen_determinant_line_bundle
Type of surface in algebraic geometry
Chern number of a rank 2 vector bundle on a surface is the number of zeroes of a generic section. For a Fano surface S, a 1-form w defines also a hyperplane
Fano_surface
Conjecture pertaining to finite covers of 3-manifold subfields
3-manifold with infinite fundamental group has a finite cover which is a surface bundle over the circle. A 3-manifold which has such a finite cover is said
Virtually_fibered_conjecture
24 mathematical problems stated in 1982
conjecture: every hyperbolic 3-manifold have a finite cover which is a surface bundle over the circle. Solved by Ian Agol. 2013 19th Describe topology and
Thurston's_24_questions
Continuous surjection satisfying a local triviality condition
In mathematics, and particularly topology, a fiber bundle (Commonwealth English: fibre bundle) is a space that is locally a product space, but globally
Fiber_bundle
of the Surface devices, the initial release of the Surface and Surface Pro had bundle options, which bundled the black Touch Cover. The Surface Pen has
List of Microsoft Surface accessories
List_of_Microsoft_Surface_accessories
Type of smooth complex surface of kodaira dimension 0
"K3 surface" In mathematics, a complex analytic K3 surface is a compact connected complex manifold of dimension 2 with а trivial canonical bundle and
K3_surface
Fiber bundle whose fibers are projective spaces
O*) only if the projective bundle is the projectivization of a vector bundle. In particular, if X is a compact Riemann surface then H2(X,O*)=0, and so this
Projective_bundle
Mathematic theorem about Riemann surfaces
Narasimhan and Seshadri (1965), says that a holomorphic vector bundle over a compact Riemann surface is stable if and only if it comes from an irreducible projective
Narasimhan–Seshadri_theorem
Ruled surface over the projective line
{\mathcal {O}}(1)} , the invertible sheaf or line bundle with associated Cartier divisor a single point. The surface Σ 0 {\displaystyle \Sigma _{0}} is isomorphic
Hirzebruch_surface
Group of isotopy classes of a topological automorphism group
in Thurston's theory of geometric three-manifolds (for example, to surface bundles). The elements of this group have also been studied by themselves:
Mapping_class_group
Principal fiber bundle
bundle is a fiber bundle where the fiber is the circle S 1 {\displaystyle S^{1}} . Oriented circle bundles are also known as principal U(1)-bundles,
Circle_bundle
Mathematical space
I-bundles Knot and link complements Lens space Seifert fiber spaces, Circle bundles Spherical 3-manifold Surface bundles over the circle Torus bundle A
3-manifold
Differentiable function whose derivative is everywhere injective
normal bundles plus trivial bundles, and thus if the stable normal bundle has cohomological dimension k, it cannot come from an (unstable) normal bundle of
Immersion_(mathematics)
decomposition Branched surface Lamination Examples 3-sphere Torus bundles Surface bundles over the circle Graph manifolds Knot complements Whitehead manifold
List of geometric topology topics
List_of_geometric_topology_topics
Fiber bundle Principal bundle Frame bundle Hopf bundle Associated bundle Vector bundle Tangent bundle Cotangent bundle Line bundle Jet bundle Sheaf (mathematics)
List of differential geometry topics
List_of_differential_geometry_topics
Anatomical cardiac structure
In the heart's conduction system, Bachmann's bundle (also called the Bachmann bundle or the interatrial band) is a branch of the anterior internodal tract
Bachmann's_bundle
of I-bundles when the base manifold is any surface but the Klein bottle K {\displaystyle K} . That surface has three I-bundles: the trivial bundle K ×
I-bundle
Correspondsnce between Higgs bundles and fundamental group representations
correspondence between stable vector bundles and unitary representations of the fundamental group of a compact Riemann surface. In fact the Narasimhan–Seshadri
Nonabelian Hodge correspondence
Nonabelian_Hodge_correspondence
sets of sections of the Horrocks–Mumford bundle are abelian surfaces of degree 10, called Horrocks–Mumford surfaces. By computing Chern classes one sees that
Horrocks–Mumford_bundle
Manifold of dimension 3 equipped with a hyperbolic metric
hyperbolic metric of finite volume. A particular case is that of a surface bundle over the circle: such manifolds are always irreducible, and they carry
Hyperbolic_3-manifold
Intrinsic geometric structures in mathematics
form with principal bundles only in the 1950s. The classical nineteenth century approach to the differential geometry of surfaces, due in large part to
Riemannian connection on a surface
Riemannian_connection_on_a_surface
Concept in algebraic geometry
geometry, a line bundle on a projective variety is nef if it has nonnegative degree on every curve in the variety. The classes of nef line bundles are described
Nef_line_bundle
Construction of combinatorial group theory
that has been 'glued back' on itself by a mapping f : X → X (see e.g. Surface bundle over the circle). Thus, HNN extensions describe the fundamental group
HNN_extension
Vector bundles theorem
(projectively) flat connection over the Riemann surface. The notion of a Hermitian–Einstein connection for a vector bundle over a higher dimensional complex manifold
Kobayashi–Hitchin correspondence
Kobayashi–Hitchin_correspondence
Aspect of heart function
the right atrium to the atrioventricular node, along the bundle of His, and through the bundle branches to Purkinje fibers in the walls of the ventricles
Cardiac_conduction_system
One-dimensional complex manifold
positive line bundle on any complex curve. The existence of non-constant meromorphic functions can be used to show that any compact Riemann surface is a projective
Riemann_surface
Electric conductors in heart ventricles
The bundle branches, or Tawara branches, transmit cardiac action potentials (electrical signals) from the bundle of His to Purkinje fibers in heart ventricles
Bundle_branches
Mathematical concept
how elliptic surfaces fit into the classification of surfaces, it is important to compute the canonical bundle of a minimal elliptic surface f: X → S. Over
Elliptic_surface
divided into two subtypes: primary Kodaira surfaces with trivial canonical bundle, and secondary Kodaira surfaces which are quotients of these by finite groups
Kodaira_surface
Construct allowing differentiation of tangent vector fields of manifolds
simplest methods of defining differentiation of the sections of vector bundles. The notion of an affine connection has its roots in 19th-century geometry
Affine_connection
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)
Relation between genus, degree, and dimension of function spaces over surfaces
holomorphic line bundles on a Riemann surface, the theorem can also be stated in a different, yet equivalent way: let L be a holomorphic line bundle on X. Let
Riemann–Roch_theorem
Concept in algebraic geometry
an ample line bundle, although there are several related classes of line bundles. Roughly speaking, positivity properties of a line bundle are related to
Ample_line_bundle
Organ found in humans and other animals
atrioventricular node only. The signal then travels along the bundle of His to left and right bundle branches through to the ventricles of the heart. In the
Heart
Circulation of blood in the blood vessels of the heart muscle (myocardium)
not give rise to a vessel. Coronary vessel branches that remain on the surface of the heart and follow the sulci of the heart are called epicardial coronary
Coronary_circulation
Mathematics theory
to the existence of a canonical indigenous bundle over the Riemann surface: the unique indigenous bundle that is invariant under complex conjugation
P-adic_Teichmüller_theory
Type of fiber bundle on a Riemann surface
indigenous bundle on a Riemann surface is a fiber bundle with a flat connection associated to some complex projective structure. Indigenous bundles were introduced
Indigenous_bundle
Straight path on a curved surface or a Riemannian manifold
in some sense the locally shortest path (arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning
Geodesic
Concept in algebraic geometry
surfaces of degree at least 3. A del Pezzo surface is a complete non-singular surface with ample anticanonical bundle. There are some variations of this definition
Del_Pezzo_surface
Structure binding nerves and vessels
through the body. There are two types of neurovascular bundles: superficial bundles and deep bundles. As arteries do not travel within the superficial fascia
Neurovascular_bundle
principal bundles was introduced by Annamalai Ramanathan for the purpose of defining the moduli space of G-principal bundles over a Riemann surface, a generalisation
Stable_principal_bundle
Muscular tissue of heart in vertebrates
relatively slow rate between the cells. Specialized conductive cells in the bundle of His, and the Purkinje fibers are larger in diameter and conduct signals
Cardiac_muscle
Characterizes homeomorphisms of a compact orientable surface
pseudo-Anosov. The case where S is a torus (i.e., a surface whose genus is one) is handled separately (see torus bundle) and was known before Thurston's work. If
Nielsen–Thurston classification
Nielsen–Thurston_classification
X^{2}+aXY+bY^{2}=P(T).\,} Conic bundles can be considered as either a Severi–Brauer or Châtelet surface. This can be a double covering of a ruled surface. It can be associated
Conic_bundle
Differential geometry topic
map of a surface is a function that maps each point in the surface to its normal direction, a unit vector that is orthogonal to the surface at that point
Gauss_map
Arteries transporting blood to heart muscle
Myocardium Conduction system cardiac pacemaker SA node Bachmann's bundle AV node bundle of His bundle branches Purkinje fibers Pericardial cavity Pericardial sinus
Coronary_arteries
Group of cells in the wall of the heart
system (SA node labeled 1) Schematic representation of the atrioventricular bundle Cardiac pacemaker Cardiology Heart block Sinus bradycardia Sinus tachycardia
Sinoatrial_node
Mathematics of smooth surfaces
manifold, to differential operators on the tangent bundle or frame bundle. In the case of an embedded surface, the lift to an operator on vector fields, called
Differential geometry of surfaces
Differential_geometry_of_surfaces
gives conditions for a line bundle on a projective surface to be very ample. Let D be a nef divisor on a smooth projective surface X. Denote by KX the canonical
Reider's_theorem
Inelastic cords of fibrous connective tissue connecting papillary muscles to heart valves
Myocardium Conduction system cardiac pacemaker SA node Bachmann's bundle AV node bundle of His bundle branches Purkinje fibers Pericardial cavity Pericardial sinus
Chordae_tendineae
Private network of connections between trusted peers
be accessed via a customized browser from Vidalia (aka the Tor browser bundle), or alternatively via a proxy configured to perform the same function.
Darknet
In mathematics, a Castelnuovo surface is a surface of general type such that the canonical bundle is very ample and such that c12 = 3pg − 7. Guido Castelnuovo
Castelnuovo_surface
Type of heat exchanger that uses ambient air as the cooling medium
applicable to ACHEs; reduction of effective surface area can only be achieved by valving off complete tube bundles. Where the process fluid is susceptible
Air_cooled_heat_exchanger
On the Euler characteristic of a holomorphic vector bundle on a compact complex manifold
class of the tangent bundle of X. Significant special cases are when E is a complex line bundle, and when X is an algebraic surface (Noether's formula)
Hirzebruch–Riemann–Roch theorem
Hirzebruch–Riemann–Roch_theorem
vector bundle is a (holomorphic or algebraic) vector bundle that is stable in the sense of geometric invariant theory. Any holomorphic vector bundle may
Stable_vector_bundle
Double-walled sac containing the heart and roots of the great vessels
the bottom (where only the serous pericardium exists to cover the upper surface of the central tendon of diaphragm). The fibrous pericardium is semi-rigid
Pericardium
Tablet computer from Microsoft
Surface Go 4 Bundle". www.microsoft.com. Retrieved 2025-06-21. "Microsoft Surface Go 4 Features". www.microsoft.com. Retrieved 2025-06-21. "Surface Go
Surface_Go_4
Equivalently it is a section of a certain line bundle on the Riemann surface in the same component as the canonical bundle. Prym differentials were introduced by
Prym_differential
Class of annelid worms
movement and, in many species, act as the worm's primary respiratory surfaces. Bundles of bristles, the chaetae, project from the parapodia. However, polychaete
Polychaete
Valve in the human heart
model of Cardiac Biological Valve Prosthesis. Front of thorax, showing surface relations of bones, lungs (purple), pleura (blue), and heart (red outline)
Aortic_valve
Sensory hair in the inner ear
the hair bundle, the kinocilium is found in the center of the apical surface of the hair cell surrounded by 20-300 microvilli. During hair bundle morphogenesis
Kinocilium
In algebraic geometry, the Iitaka dimension of a line bundle L on an algebraic variety X is the dimension of the image of the rational map to projective
Iitaka_dimension
Valve in the heart connecting the left atrium and left ventricle
tissue that thickens the spongiosa layer of the cusp and separates collagen bundles in the fibrosa. This weakens the cusps and adjacent tissue, resulting in
Mitral_valve
Part of the human heart
right auricle, lat: auricula atrii dextra) is located at the front upper surface of the right atrium. Looking from the front, the right atrial appendage
Atrium_(heart)
Network of cells that facilitate rhythmic heart contraction
ventricles known as the atrioventricular junction. The Bundle of His transmits signals to the bundle branches, which send them on to the Purkinje fibers
Natural_pacemaker
Concept in algebraic geometry
Kunihiko Kodaira. The canonical bundle of a smooth algebraic variety X of dimension n over a field is the line bundle of n-forms, K X = ⋀ n Ω X 1 , {\displaystyle
Kodaira_dimension
Mathematics concept
neighborhood of an orientable surface in an orientable 3-manifold is just a "thickened up" version of the surface, i.e., a trivial I-bundle. So the regular neighborhood
Haken_manifold
Mathematical classification of surfaces
Hirzebruch surfaces Σn for n = 0 or n ≥ 2. (The Hirzebruch surface Σn is the P1 bundle over P1 associated to the sheaf O(0) + O(n). The surface Σ0 is isomorphic
Enriques–Kodaira classification
Enriques–Kodaira_classification
In Euclidean geometry, the bundle theorem is a statement about six circles and eight points in the Euclidean plane. In general incidence geometry, it is
Bundle_theorem
Cleaning tool made up of coarse strings
A mop (such as a floor mop) is a mass or bundle of coarse strings or yarn, etc., or a piece of cloth, sponge or other absorbent material, attached to a
Mop
Algebraic surface with special triviality properties
In mathematics, Enriques surfaces are algebraic surfaces such that the irregularity q = 0 and the canonical line bundle K is non-trivial but has trivial
Enriques_surface
Fibre secreted by some molluscs
(/ˈbɪsəs/) is a bundle of filaments secreted by many species of bivalve mollusc that function to attach the mollusc to a solid surface. Species from several
Byssus
Mathematical theorem
the trivial bundle, and is equal to 1 + p a {\displaystyle 1+p_{a}} , where p a {\displaystyle p_{a}} is the arithmetic genus of the surface. For comparison
Riemann–Roch theorem for surfaces
Riemann–Roch_theorem_for_surfaces
Digital pen made by Microsoft
strokes when it comes into contact with the display. It was bundled with the Surface Pro and Surface Pro 2, but is not compatible with other models. The button
Surface_Pen
Muscle band in the right ventricle of the heart
moderator band consists of conductive tissue branching off of the right bundle branch (within the ventricular septum) and wrapped in working cardiac muscle
Moderator_band
List of algebraic surfaces Ruled surface Cubic surface Veronese surface Del Pezzo surface Rational surface Enriques surface K3 surface Hodge index theorem
List of algebraic geometry topics
List_of_algebraic_geometry_topics
High frequency optimised electric wire
several levels of bundling (already-twisted wires are twisted together into small bundles, which are then twisted into larger bundles, etc.). The result
Litz_wire
Feature of chordate cardiac anatomy
from the right atrioventricular fibrous ring and connects the posterior surface of the infundibulum to the aorta. The infundibulum is the entrance from
Infundibulum_(heart)
Electrical conducting structure in the heart
(October 1972). "Arterial blood supply of the atrioventricular node and main bundle". British Heart Journal. 34 (10): 1045–1051. doi:10.1136/hrt.34.10.1045
Atrioventricular_node
Surface containing a line through every point
projective bundle of a 2-dimensional vector bundle over some curve. The ruled surfaces with base curve of genus 0 are the Hirzebruch surfaces. Doubly ruled
Ruled_surface
Chamber of the heart
adult. Its upper front surface is circled and convex, and forms much of the sternocostal surface of the heart. Its under surface is flattened, forming
Ventricle_(heart)
Ligaments of the sternum and pericardium
The fibrous pericardium is attached to the posterior surface of the sternum by the superior and inferior sternopericardiac ligaments (sternopericardial
Sternopericardial_ligaments
Star's outer shell from which light is radiated
star's outer shell from which light is radiated. It extends into a star's surface until the plasma becomes opaque, equivalent to an optical depth of approximately
Photosphere
Algebraic surface
has degree 3 or 4. They are conic bundles. Châtelet, F. (1959), "Points rationnels sur certaines courbes et surfaces cubiques", L'Enseignement mathématique
Châtelet_surface
) {\displaystyle \operatorname {Pic} ^{0}(A)} is called a degree 0 line bundle on A. To A one then associates a dual abelian variety Av (over the same
Dual_abelian_variety
Laptop by Microsoft
while the base has 8-hour. The Surface Book's keyboard is considered a standard component of the device, and is bundled with all models. The device consists
Surface_Book
Muscular columns found in the heart
are rounded or irregular muscular columns which project from the inner surface of the right and left ventricle of the heart. These are different from
Trabeculae_carneae
Diffeomorphism that has a hyperbolic structure on the tangent bundle
tangent bundle of 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
Anosov_diffeomorphism
Serous fluid within the pericardial cavity of the heart
reduces friction within the pericardium by lubricating the epicardial surface allowing the membranes to glide over each other with each heart beat. Ben-Horin
Pericardial_fluid
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