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Topological Hochschild
homology of Thom spectra and the free loop space
Andrew J Blumberg, Ralph L Cohen and Christian Schlichtkrull |
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Geometry & Topology 14 (2010) 1165–1242
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Abstract |
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We describe the topological Hochschild homology of ring spectra that arise as Thom spectra for loop maps , where denotes the classifying space for stable spherical fibrations. To do this, we consider symmetric monoidal models of the category of spaces over 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 . This leads to explicit calculations of the topological Hochschild homology for a large class of ring spectra, including all of the classical cobordism spectra , , , etc, and the Eilenberg–Mac Lane spectra and . |
Keywords
topological Hochschild homology, Thom spectra, loop space
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Mathematical Subject Classification 2000
Primary: 19D55, 55N20
Secondary: 18G55, 55P43, 55P47, 55R25
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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
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Authors |
| Andrew J Blumberg | |
| Department of Mathematics Stanford University Stanford, CA 94305 United States |
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| Ralph L Cohen | |
| Department of Mathematics Stanford University Stanford, CA 94305 United States |
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| Christian Schlichtkrull | |
| Department of Mathematics University of Bergen Johannes Brunsgate 12 5008 Bergen Norway |
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