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THH of Thom spectra that are E_infty ring spectra | | Andrew J. Blumberg
; | | Date: |
5 Nov 2008 | | Abstract: | We identify the topological Hochschild homology (THH) of the Thom spectrum
associated to an E_infty 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_infty 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_infty map,
provided that the induced multiplication on Mf extends to an E_infty ring
structure; this permits us to recover Bokstedt’s calculation of THH(HZ). | | Source: | arXiv, 0811.0803 | | Services: | Forum | Review | PDF | Favorites | |
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