GENERALIZED THOM SPECTRA AND THEIR TOPOLOGICAL HOCHSCHILD HOMOLOGY

We develop a theory of $R$ -module Thom spectra for a commutative symmetric ring spectrum $R$ and we analyze their multiplicative properties. As an interesting source of examples, we show that $R$ -algebra Thom spectra associated to the special unitary groups can be described in terms of quotient co...

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Bibliographic Details
Published in:Journal of the Institute of Mathematics of Jussieu 2020-01, Vol.19 (1), p.21-64
Main Authors: Basu, Samik, Sagave, Steffen, Schlichtkrull, Christian
Format: Article
Language:English
Subjects:
Algebra
Homology
Quotients
Rings (mathematics)
Spectra
Topology
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Summary:We develop a theory of $R$ -module Thom spectra for a commutative symmetric ring spectrum $R$ and we analyze their multiplicative properties. As an interesting source of examples, we show that $R$ -algebra Thom spectra associated to the special unitary groups can be described in terms of quotient constructions on $R$ . We apply the general theory to obtain a description of the $R$ -based topological Hochschild homology associated to an $R$ -algebra Thom spectrum.
ISSN:1474-7480
1475-3030
DOI:10.1017/S1474748017000421