Topic
Fiber bundle
About: Fiber bundle is a research topic. Over the lifetime, 3045 publications have been published within this topic receiving 39579 citations. The topic is also known as: fibre bundle.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: In this article, a projectively flat connection on the quantum Hubert bundle over Teichmuller space is constructed for affine symplectic quotients, and the connection is expressed in terms of the intrinsic Kahler geometry of the quotient and the Quillen connection.
Abstract: We present a new construction of the quantum Hubert space of ChernSimons gauge theory using methods which are natural from the threedimensional point of view. To show that the quantum Hubert space associated to a Riemann surface Σ is independent of the choice of complex structure on Σ, we construct a natural projectively flat connection on the quantum Hubert bundle over Teichmuller space. This connection has been previously constructed in the context of two-dimensional conformal field theory where it is interpreted as the stress energy tensor. Our construction thus gives a (2 + 1 )-dimensional derivation of the basic properties of (1 + 1)-dimensional current algebra. To construct the connection we show generally that for affine symplectic quotients the natural projectively flat connection on the quantum Hubert bundle may be expressed purely in terms of the intrinsic Kahler geometry of the quotient and the Quillen connection on a certain determinant line bundle. The proof of most of the properties of the connection we construct follows surprisingly simply from the index theorem identities for the curvature of the Quillen connection. As an example, we treat the case when Σ has genus one explicitly. We also make some preliminary comments concerning the Hubert space structure.
511 citations
TL;DR: In this paper, Mumford showed that the Picard group P ic (~') is isomorphic to H2(F; 2~) and conjectured the latter is rank one, g>3.
Abstract: In I-7] Mumford shows that the Picard group P ic (~ ' ) is isomorphic to H2(F; 2~) and conjectures the latter is rank one, g>3 . We prove this below for g>5 . Another interpretation of this theorem may be obtained by identifying H2(F) as bordism classes of fiber bundles F---*W4---* T where T is a closed oriented surface (Sect. 0). When F is closed every such bundle is bordant to F ~ W' --* T', a bundle admitting a section s: T ' ~ W'. The theorem then says that
422 citations
Book•
1 Jan 1984
TL;DR: In this paper, differentiable manifold bundles and folial bundles are used to represent the topology of the leaves of a group of leaves in a group action model, and Frobenius' theorem is proved.
Abstract: I - Differentiable Manifolds.- II - Foliations.- III - The Topology of the Leaves.- IV - Holonomy and the Stability Theorems.- V - Fiber Bundles and Foliations.- VI - Analytic Foliations of Codimension One.- VII - Novikov's Theorem.- VIII - Topological Aspects of the Theory of Group Actions.- Appendix - Frobenius' Theorem.- 1. Vector fields and the Lie bracket.- 2. Frobenius' theorem.- 3. Plane fields defined by differential forms.- Exercises.
405 citations
TL;DR: In this article, the authors find an interpretation of the recent connection found between topological strings on Calabi-Yau threefolds and crystal melting: summing over statistical mechanical configuration of melting crystal is equivalent to a quantum gravitational path integral involving fluctuations of Kahler geometry and topology.
Abstract: We find an interpretation of the recent connection found between topological strings on Calabi-Yau threefolds and crystal melting: Summing over statistical mechanical configuration of melting crystal is equivalent to a quantum gravitational path integral involving fluctuations of Kahler geometry and topology. We show how the limit shape of the melting crystal emerges as the average geometry and topology of the quantum foam at the string scale. The geometry is classical at large length scales, modified to a smooth limit shape dictated by mirror geometry at string scale and is a quantum foam at area scales ~ gsα'.
392 citations
Abstract: We apply a modified Yang-Mills-Higgs functional to unitary bundles over closed Kahler manifolds and study the equations which govern the global minima. The solutions represent vortices in holomorphic bundles and are direct analogs of the vortices overR
2. We obtain a complete description of the moduli space of these new vortices where the bundle is of rank one. The description is in terms of a class of divisors in the base manifold. There is also a dependence on a real valued parameter which can be attributed to the compactness of the base manifold.
391 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 46 |
| 2024 | 41 |
| 2023 | 71 |
| 2022 | 185 |
| 2021 | 68 |
| 2020 | 106 |