∞-Bundles

Severin Bunk

doi:10.1016/B978-0-323-95703-8.00208-1

∞-Bundles

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Abstract

Higher bundles are homotopy-coherent generalizations of classical fiber bundles. They appear in numerous contexts in geometry, topology and physics. In particular, higher principal bundles provide the geometric framework for higher-group gauge theories with higher-form gauge potentials and their higher-dimensional holonomies. An ∞-categorical formulation of higher bundles further allows one to identify these objects in contexts outside the worlds of smooth manifolds or topological spaces. This article reviews the theory of ∞-bundles, focussing on principal ∞-bundles, and surveys several of their applications. It is an invited contribution to the Topology section in the second edition of the Encyclopedia of Mathematical Physics.

Original language	English
Title of host publication	Encyclopedia of Mathematical Physics (Second Edition)
Editors	Richard Szabo, Martin Bojowald
Publisher	Elsevier
Pages	77-97
Number of pages	20
Volume	4
Edition	2
ISBN (Print)	978-0-323-95706-9
DOIs	https://doi.org/10.1016/B978-0-323-95703-8.00208-1
Publication status	E-pub ahead of print - 3 Oct 2024

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N2 - Higher bundles are homotopy-coherent generalizations of classical fiber bundles. They appear in numerous contexts in geometry, topology and physics. In particular, higher principal bundles provide the geometric framework for higher-group gauge theories with higher-form gauge potentials and their higher-dimensional holonomies. An ∞-categorical formulation of higher bundles further allows one to identify these objects in contexts outside the worlds of smooth manifolds or topological spaces. This article reviews the theory of ∞-bundles, focussing on principal ∞-bundles, and surveys several of their applications. It is an invited contribution to the Topology section in the second edition of the Encyclopedia of Mathematical Physics.

AB - Higher bundles are homotopy-coherent generalizations of classical fiber bundles. They appear in numerous contexts in geometry, topology and physics. In particular, higher principal bundles provide the geometric framework for higher-group gauge theories with higher-form gauge potentials and their higher-dimensional holonomies. An ∞-categorical formulation of higher bundles further allows one to identify these objects in contexts outside the worlds of smooth manifolds or topological spaces. This article reviews the theory of ∞-bundles, focussing on principal ∞-bundles, and surveys several of their applications. It is an invited contribution to the Topology section in the second edition of the Encyclopedia of Mathematical Physics.

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BT - Encyclopedia of Mathematical Physics (Second Edition)

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ER -

∞-Bundles

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