Generalized Thom spectra and their topological Hochschild homology

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.