Generalized Thom spectra and their topological Hochschild homology

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.

v2: 38 pages, minor revision. Accepted for publication in J. Inst. Math. Jussieu

References in corpus (1)

• An $\infty$-categorical approach to $R$-line bundles, $R$-module Thom spectra, and twisted $R$-homology

Cited by in corpus (3)

• Multiplicative parametrized homotopy theory via symmetric spectra in retractive spaces
• Homotopical and operator algebraic twisted K-theory
• Thom spectra, higher $THH$ and tensors in $\infty$-categories