## Topological Hochschild homology of Thom spectra which are . . . (2008)

Citations: | 8 - 2 self |

### BibTeX

@MISC{Blumberg08topologicalhochschild,

author = {Andrew J. Blumberg},

title = { Topological Hochschild homology of Thom spectra which are . . . },

year = {2008}

}

### OpenURL

### Abstract

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) ≃ Mf ∧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).