arXiv:1912.10544 Abstract | arXiv Analytics

arXiv:1912.10544 [math.AT]Abstract References Reviews Resources

Classifying spaces of infinity-sheaves

Daniel Berwick-Evans, Pedro Boavida de Brito, Dmitri Pavlov

Published 2019-12-22Version 1

We prove that the set of concordance classes of sections of an infinity-sheaf on a manifold is representable, extending a theorem of Madsen and Weiss. 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?

Comments: 31 pages. Comments are very welcome

Categories: math.AT, math.CT, math.KT

Subjects: 55N30, 57R19, 55N20, 18G60, 22A22, 18F10, 18F20, 14D23, 14A20, 58D27, 58D29, 14D22, 55R35, 55U35, 18G55, 14F42, 55R65

Keywords: classifying space, infinity-sheaf, concordance classes, reminiscent, h-principle

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