The Dold−Thom theorem via factorization homology
The Dold−Thom theorem is a classical result in algebraic topology relating homotopy and homology. It states that for a nice topological space M, there are isomorphisms between the homotopy groups of the infinite symmetric product of M and the reduced homology groups of M itself: π∗(Sym(M;A))≅˜H∗(M;A). The classical proof appeals to the Eilenberg−Steenrod axioms to verify the composition of functors π∗(Sym(−;A)) determines the same homology theory as reduced singular homology. In this talk, we will outline a new, direct proof of the Dold−Thom theorem which avoids the Eilenberg−Steenrod axioms entirely. The heart of this proof is a local-to-global argument allowing us to recognize the infinite symmetric product as an instance of factorization homology.