Classifying spaces of infinity-sheaves
Algebraic Topology
2025-02-26 v3 Category Theory
K-Theory and Homology
Abstract
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?
Keywords
Cite
@article{arxiv.1912.10544,
title = {Classifying spaces of infinity-sheaves},
author = {Daniel Berwick-Evans and Pedro Boavida de Brito and Dmitri Pavlov},
journal= {arXiv preprint arXiv:1912.10544},
year = {2025}
}
Comments
35 pages. Comments are very welcome. v2: Many expository improvements. v3: Identical to the journal version except for formatting and style