GENERALIZED THOM SPECTRA AND THEIR TOPOLOGICAL HOCHSCHILD HOMOLOGY. (2nd November 2017)

• Record Type: Journal Article
• Authors: Basu, Samik; Sagave, Steffen; Schlichtkrull, Christian
• Is Part Of: Journal of the Institute of Mathematics of Jussieu. Volume 19:Number 1(2020)
• Page Start: 21
• Page End: 64
• Publication Date: 2017-11-02
• Subjects: 19D55, -- 55N20, -- 55P42, -- 55P43, -- 55P48; Thom spectrum, -- structured ring spectrum, -- topological Hochschild homology; Mathematics -- Periodicals; 510.5
• DOI: 10.1017/S1474748017000421
• Languages: English
• ISSNs: 1474-7480

Abstract

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.