TY - JOUR
T1 - Classifying spaces of infinity-sheaves
AU - Berwick-Evans, Daniel
AU - BOAVIDA DE BRITO, Pedro
AU - Pavlov, Dmitri
N1 - Publisher Copyright:
© 2024 The Authors, under license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open.
PY - 2024
Y1 - 2024
N2 - 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 h–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?.
AB - 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 h–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?.
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U2 - 10.2140/agt.2024.24.4891
DO - 10.2140/agt.2024.24.4891
M3 - Article
AN - SCOPUS:85214886980
SN - 1472-2747
VL - 24
SP - 4891
EP - 4937
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
IS - 9
ER -