2017/03/27 by Lauren Bandklayder, Bandklayder, Lauren
Mathematics · Physics and Astronomy · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1703.09170
openalex publication_date 2017/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.