Triangulation of Fibre Bundles

1967 ◽  
Vol 19 ◽  
pp. 499-513 ◽  
Author(s):  
H. Putz
Keyword(s):  
Vector Bundles ◽  
Fibre Bundle ◽  
Base Space ◽  
Total Space ◽  
Fibre Bundles ◽  
Differentiable Manifolds ◽  
Geometric Methods

In this paper we consider the following problem. Let (E, M, N, π) be a differentiable fibre bundle, whereEis the total space,Mthe base space,Nthe fibre, andπ: E→Mthe projection map. Then, given aCrtriangulation (ƒ, D) ofM,can one obtain aCrtriangulation (F, K) ofEsuch that the induced mapƒ–1πF:K→ D is linear? R. Lashof and M. Rothenberg (3) have obtained this result for vector bundles.Using methods quite different from theirs, we obtain a solution in the general case. The methods we use are the geometric methods developed by J. H. C. Whitehead. (7) in his triangulation of differentiable manifolds, as found in (5). In fact, our solution consists of generalizing his techniques in a fibre bundle setting.

scholarly journals Dispersive semiflows on fiber bundles

2017 ◽  
Vol 37 (2) ◽  
pp. 85-99
Author(s):  
Josiney A. Souza ◽  
Hélio V. M. Tozatti
Keyword(s):  
Periodic Point ◽  
Fiber Bundle ◽  
Vector Bundles ◽  
Base Space ◽  
Total Space ◽  
Fiber Bundles ◽  
Almost Periodic ◽  
Special Result ◽  
Almost Periodic Point

This paper studies dispersiveness of semiflows on fiber bundles. The main result says that a right invariant semiflow on a fiber bundle is dispersive on the base space if and only if there is no almost periodic point and the semiflow is dispersive on the total space. A special result states that linear semiflows on vector bundles are not dispersive.

scholarly journals Generalized vanishing theorems for Yukawa couplings in heterotic compactifications

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Lara B. Anderson ◽  
James Gray ◽  
Magdalena Larfors ◽  
Matthew Magill ◽  
Robin Schneider
Keyword(s):  
Vector Bundles ◽  
Geometric Approach ◽  
Low Energy ◽  
Geometric Features ◽  
Vanishing Theorems ◽  
Vanishing Theorem ◽  
Alternative Derivation ◽  
Yukawa Couplings ◽  
Geometric Methods ◽  
Higher Dimensional

Abstract Heterotic compactifications on Calabi-Yau threefolds frequently exhibit textures of vanishing Yukawa couplings in their low energy description. The vanishing of these couplings is often not enforced by any obvious symmetry and appears to be topological in nature. Recent results used differential geometric methods to explain the origin of some of this structure [1, 2]. A vanishing theorem was given which showed that the effect could be attributed, in part, to the embedding of the Calabi-Yau manifolds of interest inside higher dimensional ambient spaces, if the gauge bundles involved descended from vector bundles on those larger manifolds. In this paper, we utilize an algebro-geometric approach to provide an alternative derivation of some of these results, and are thus able to generalize them to a much wider arena than has been considered before. For example, we consider cases where the vector bundles of interest do not descend from bundles on the ambient space. In such a manner we are able to highlight the ubiquity with which textures of vanishing Yukawa couplings can be expected to arise in heterotic compactifications, with multiple different constraints arising from a plethora of different geometric features associated to the gauge bundle.

scholarly journals SCATTERING, GREEN’S FUNCTIONS AND SYMMETRIES IN A TOTAL SPACE OF A DIRAC MONOPOLE FIBRE BUNDLE

1991 ◽  
Vol 06 (04) ◽  
pp. 577-598 ◽  
Author(s):  
A.G. SAVINKOV ◽  
A.B. RYZHOV
Keyword(s):  
Green's Functions ◽  
Principal Bundle ◽  
Fibre Bundle ◽  
Green’S Functions ◽  
Wave Functions ◽  
Total Space ◽  
Dirac Monopole ◽  
Hidden Symmetries ◽  
Scattering Wave ◽  
A Charge

The scattering wave functions and Green’s functions were found in a total space of a Dirac monopole principal bundle. Also, hidden symmetries of a charge-Dirac monopole system and those joining the states relating to different topological charges n=2eg were found.

Differentiable Manifolds with an Area Measure

1967 ◽  
Vol 19 ◽  
pp. 540-549 ◽  
Author(s):  
F. Brickell
Keyword(s):  
Fibre Bundle ◽  
Area Measure ◽  
Differentiable Manifolds ◽  
Linearly Independent ◽  
Class C ◽  
Definition Of

In this section we fix some notations and give a definition of an area measure on a differentiate manifold, where throughout the paper the word differentiable implies differentiability of class C∞. LetMdenote a differentiate manifold of dimensionnand call a set ofmlinearly independent vectors{e1,… ,em} at a point ofManm-frame ofM.The setE′of all suchm-frames can be given the structure of a differentiable fibre bundle overMand we denote the projection ofE'ontoMbyπ′.

Vector bundles that fill n-space

1965 ◽  
Vol 61 (4) ◽  
pp. 869-875 ◽  
Author(s):  
S. A. Robertson ◽  
R. L. E. Schwarzenberger
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Total Space

The idea of exact filling bundle may be described roughly as follows. Suppose that ξk is a vector bundle with fibre Rk, total space E(ξk) and base X. We say that ξk is a real k-plane bundle on X. Let in be the trivial n-plane bundle on X so that E(in) = X × Rn. A bundle monomorphism j: ξk → in defines a map : E(ξk)→Rn obtained by composition of the embedding E(ξk)→E(in) and the product projection E(in) → Rn. The map represents each fibre of ξk as a k-plane in Rn.

Equivariant Maps from Stiefel Bundles to Vector Bundles

2016 ◽  
Vol 60 (1) ◽  
pp. 231-250 ◽  
Author(s):  
Mahender Singh
Keyword(s):  
Vector Bundle ◽  
Lower Bound ◽  
Vector Bundles ◽  
Fibre Bundle ◽  
Cohomological Dimension ◽  
Stiefel Manifold ◽  
Zero Section ◽  
Zero Set ◽  
Compact Lie Group ◽  
Equivariant Maps

AbstractLet E → B be a fibre bundle and let Eʹ → B be a vector bundle. Let G be a compact Lie group acting fibre preservingly and freely on both E and Eʹ – 0, where 0 is the zero section of Eʹ → B. Let f : E → Eʹ be a fibre-preserving G-equivariant map and let Zf = {x ∈ E | f(x) = 0} be the zero set of f. In this paper we give a lower bound for the cohomological dimension of the zero set Zf when a fibre of E → B is a real Stiefel manifold with a free ℤ/2-action or a complex Stiefel manifold with a free 𝕊1-action. This generalizes a well-known result of Dold for sphere bundles equipped with free involutions.

scholarly journals Translations as gauge transformations

1977 ◽  
Vol 20 (1) ◽  
pp. 38-45 ◽  
Author(s):  
P. K. Smrz
Keyword(s):  
Cross Sections ◽  
Fibre Bundle ◽  
Mass Term ◽  
De Sitter ◽  
Fibre Bundles ◽  
Gauge Transformations ◽  
Interaction Terms ◽  
Local Description ◽  
Minkowski Space Time ◽  
Dirac Wave Function

AbstractA local description of space and time in which translations are included in the group of gauge transformations is studied using the formalism of fibre bundles. It is shown that the flat Minkowski space–time may be obtained from a non-flat connection in a de Sitter structured fibre bundle by choosing at least two different cross-sections. The interaction terms in the covariant derivative of a Dirac wave function that correspond to translations may be interpreted as the mass term of the Dirac equation, and then the two cross-sections (gauges) correspond to the description of a fermion and antifermion respectively.

Gromov–Witten type invariants on circle bundles over symplectic manifolds

2016 ◽  
Vol 13 (09) ◽  
pp. 1650114
Author(s):  
Yong Seung Cho ◽  
Young Do Chai
Keyword(s):  
Moduli Space ◽  
Contact Structure ◽  
Quantum Cohomology ◽  
Symplectic Manifolds ◽  
Base Space ◽  
Total Space ◽  
Witten Invariant ◽  
Circle Bundles ◽  
Type Invariant ◽  
The One

We consider circle bundles over symplectic manifolds to study Gromov–Witten type invariants. We investigate the moduli space of pseudo-coholomorphic maps, Gromov–Witten type invariant, the quantum type cohomology of the total space which has a natural contact structure. We then compare Gromov–Witten invariant, and quantum cohomology of the base space with the one of the total space, and derive some relations between them.

scholarly journals Bi-slant submersions in complex geometry

2020 ◽  
Vol 17 (04) ◽  
pp. 2050055
Author(s):  
Cem Sayar ◽  
Mehmet Akif Akyol ◽  
Rajendra Prasad
Keyword(s):  
Riemannian Manifolds ◽  
Complex Geometry ◽  
Base Space ◽  
Total Space ◽  
Riemannian Submersions ◽  
Kaehler Manifolds ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds

In this paper, we introduce bi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalization of invariant, anti-invariant, semi-invariant, slant, semi-slant and hemi-slant Riemannian submersions. We mainly focus on bi-slant submersions from Kaehler manifolds. We provide a proper example of bi-slant submersion, investigate the geometry of foliations determined by vertical and horizontal distributions, and obtain the geometry of leaves of these distributions. Moreover, we obtain curvature relations between the base space, the total space and the fibers, and find geometric implications of these relations.

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