2008/11/05 by Andrew J. Blumberg, Blumberg, Andrew J.
Mathematics · #55N20 #55P43 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:55N20 #msc:55P43
paper · pdf · doi:10.48550/arxiv.0811.0803
arxiv created 2008/11/05 · openalex publication_date 2008/11/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We identify the topological Hochschild homology (THH) of the Thom spectrum associated to an E_∞ classifying map X -> BG, for G an appropriate group or monoid (e.g. U, O, and F). We deduce the comparison from the observation of McClure, Schwanzl, and Vogt that THH of a cofibrant commutative S-algebra (E_∞ ring spectrum) R can be described as an indexed colimit together with a verification that the Lewis-May operadic Thom spectrum functor preserves indexed colimits. We prove a splitting result THH(Mf) \htp Mf \sma BX+ which yields a convenient description of THH(MU). This splitting holds even when the classifying map f: X -> BG is only a homotopy commutative A_∞ map, provided that the induced multiplication on Mf extends to an E_∞ ring structure; this permits us to recover Bokstedt's calculation of THH(HZ).