Classifying spaces of infinity-sheaves

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?

35 pages. Comments are very welcome. v2: Many expository improvements. v3: Identical to the journal version except for formatting and style

References in corpus (6)

• Higher Topos Theory
• Embeddings from the point of view of immersion theory: Part I
• Differential cohomology in a cohesive infinity-topos
• Numerable open covers and representability of topological stacks
• Another approach to the Kan-Quillen model structure
• Projective model structures on diffeological spaces and smooth sets and the smooth Oka principle

Cited by in corpus (2)

• Principal $\infty$-Bundles and Smooth String Group Models
• The $\mathbb{R}$-Local Homotopy Theory of Smooth Spaces