Topological Hochschild homology of Thom spectra and the free loop space

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.

58 pages

References in corpus (4)

• Diagram spaces and symmetric spectra
• Units of ring spectra and Thom spectra
• Higher topological Hochschild homology of Thom spectra
• Thom spectra that are symmetric spectra

Cited by in corpus (31)

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• Diagram spaces, diagram spectra, and spectra of units
• Higher topological Hochschild homology of Thom spectra
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• Group completion and units in I-spaces
• Eilenberg-MacLane spectra as equivariant Thom spectra
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• Towards an understanding of ramified extensions of structured ring spectra
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• The factorization theory of Thom spectra and twisted non-abelian Poincaré duality
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• Reflexive homology
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• The circle action on topological Hochschild homology of complex cobordism and the Brown-Peterson spectrum
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• Braided injections and double loop spaces
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• Whitehead Filtrations for Computations in Topological Hochschild Homology
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