Geometry & Topology 14 (2010) 1165–1242

DOI: 10.2140/gt.2010.14.1165

Abstract

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 explicit 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.

Keywords

topological Hochschild homology, Thom spectra, loop space

Mathematical Subject Classification

Primary: 19D55, 55N20

Secondary: 18G55, 55P43, 55P47, 55R25

References

Publication

Received: 4 November 2008
Revised: 1 March 2010
Accepted: 2 April 2010
Published: 23 May 2010
Proposed: Paul Goerss
Seconded: Bill Dwyer, Haynes Miller

Authors