A proof of the Dold$-$Thom theorem via factorization homology

Abstract

The Dold$-$Thom theorem states that for a sufficiently nice topological space, M, there is an isomorphism between the homotopy groups of the infinite symmetric product of M and the homology groups of M itself. The crux of most known proofs of this is to check that a certain map is a quasi-fibration. It is our goal to present a more direct proof of the Dold$-$Thom theorem which does appeal to any such fact. The heart of our proof lies in identification of the infinite symmetric product as an instance of factorization homology.

v2. changed typo in title; v3. added abstract, added references, made minor mathematical changes and made slightly more substantial expository changes

References in corpus (2)

• Higher Topos Theory
• Zero-pointed manifolds