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Classifying spaces of
infinity-sheaves
Daniel Berwick-Evans, Pedro Boavida de Brito and Dmitri Pavlov |
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Algebraic & Geometric Topology 24 (2024) 4891–4937
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Abstract |
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We prove that the set of concordance classes of sections of an –sheaf on a manifold is representable, extending a theorem of Madsen and Weiss for sheaves of sets. This is reminiscent of an –principle in which the role of isotopy is played by concordance. As an application, we offer an answer to the question: what does the classifying space of a Segal space classify? |
Keywords
sheaves
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Mathematical Subject Classification
Primary: 18F20, 18N60, 55N30
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References |
Publication
Received: 21 May 2022
Revised: 1 May 2023
Accepted: 5 June 2023
Published: 27 December 2024
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Authors |
| Daniel Berwick-Evans | |
| Department of Mathematics University of Illinois at Urbana–Champaign Urbana, IL United States |
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| https://danbe.web.illinois.edu/ | |
| Pedro Boavida de Brito | |
| Department of Mathematics Instituto Superior Técnico Universidade de Lisboa Lisbon Portugal |
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| https://www.math.tecnico.ulisboa.pt/~pbrito/ | |
| Dmitri Pavlov | |
| Department of Mathematics and
Statistics Texas Tech University Lubbock, TX United States |
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| https://dmitripavlov.org/ | |
| © 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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