Classifying spaces of infinity-sheaves

TL;DR

This paper proves that the set of concordance classes of sections of an infinity-sheaf on a manifold is representable, extending known theorems and connecting to the classification of Segal spaces.

Contribution

It extends the theorem of Madsen and Weiss by showing the representability of concordance classes of infinity-sheaf sections and relates to an h-principle involving concordance.

Findings

Concordance classes of infinity-sheaf sections are representable.

The work extends Madsen and Weiss's theorem.

Provides insight into the classifying space of a Segal space.

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?