Topological Hochschild homology of Thom spectra and the free loop space

Andrew J Blumberg, Ralph L Cohen, Christian Schlichtkrull
2010 Geometry and Topology  
We describe the topological Hochschild homology of ring spectra that arise as Thom spectra for loop maps f: X->BF, where BF denotes the classifying space for stable spherical fibrations. To do this, we consider symmetric monoidal models of the category of spaces over BF and corresponding strong symmetric monoidal Thom spectrum functors. Our main result identifies the topological Hochschild homology as the Thom spectrum of a certain stable bundle over the free loop space L(BX). This leads to
more » ... icit calculations of the topological Hochschild homology for a large class of ring spectra, including all of the classical cobordism spectra MO, MSO, MU, etc., and the Eilenberg-Mac Lane spectra HZ/p and HZ.
doi:10.2140/gt.2010.14.1165 fatcat:zkchcu2nwfckdgs5vudxapri3e