Generalized Thom spectra and their topological Hochschild homology
Samik Basu, Steffen Sagave, Christian Schlichtkrull

TL;DR
This paper develops a theory of R-module Thom spectra for commutative symmetric ring spectra, analyzing their multiplicative properties and applying the theory to describe R-based topological Hochschild homology of Thom spectra.
Contribution
It introduces a new framework for R-module Thom spectra and relates them to quotient constructions and topological Hochschild homology.
Findings
Thom spectra associated to special unitary groups can be described via quotient constructions.
The theory provides a way to compute R-based topological Hochschild homology for Thom spectra.
Multiplicative properties of R-module Thom spectra are characterized and analyzed.
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.
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