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GENERALIZED THOM SPECTRA AND THEIR TOPOLOGICAL HOCHSCHILD HOMOLOGY

Part of: Higher algebraic $K$-theory Homology and cohomology theories Homotopy theory

Published online by Cambridge University Press:  02 November 2017

Samik Basu ,
Steffen Sagave  and
Christian Schlichtkrull
Samik Basu
Affiliation:
Department of Mathematical and Computational Science, Indian Association for the Cultivation of Science, Kolkata - 700032, India ([email protected])
Steffen Sagave
Affiliation:
Radboud University Nijmegen, IMAPP, PO Box 9010, 6500 GL Nijmegen, The Netherlands ([email protected])
Christian Schlichtkrull
Affiliation:
Department of Mathematics, University of Bergen, P.O. Box 7803, 5020 Bergen, Norway ([email protected])
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Abstract

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.

Keywords

Thom spectrumstructured ring spectrumtopological Hochschild homology

MSC classification

Primary: 19D55: $K$-theory and homology; cyclic homology and cohomology 55N20: Generalized (extraordinary) homology and cohomology theories 55P42: Stable homotopy theory, spectra 55P43: Spectra with additional structure ($E_infty$, $A_infty$, ring spectra, etc.) 55P48: Loop space machines, operads
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 19 , Issue 1 , January 2020 , pp. 21 - 64
Copyright
© Cambridge University Press 2017 

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