Work

Classifying spaces of infinity-sheaves

Year: 2024

Type: article

Abstract: We prove that the set of concordance classes of sections of an 1-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?18F20, 18N60, 55N30 1. Introduction 4891 2. The concordance resolution is concordance-invariant 4896 3. Weak Kan fibrations 4901 4. Weak Kan fibrancy of the concordance resolution 4908 5.The shape functor preserves the 1-sheaf property 4920 6.What does the classifying space of an 1-category classify?4927 Appendix.Technical lemmas on simplicial sets and spaces 4930

Source: Algebraic & Geometric Topology

DOI: 10.2140/agt.2024.24.4891

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

Institutions: University of Illinois Urbana-Champaign, University of Lisbon, Instituto Superior Técnico, Texas Tech University

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: Fundação para a Ciência e a Tecnologia

Award: Automorphisms of manifolds, spaces of embeddings and operads