Higher topological Hochschild homology of Thom spectra

TL;DR

This paper investigates the higher topological Hochschild homology of commutative Thom spectra, including classical cobordism spectra, exploring their homotopy orbits and connections to topological Andre-Quillen homology.

Contribution

It provides new insights into the structure of higher topological Hochschild homology for Thom spectra and relates it to topological Andre-Quillen homology.

Findings

Describes the homotopy orbits of the torus action on iterated topological Hochschild homology.

Establishes relationships between higher topological Hochschild homology and topological Andre-Quillen homology.

Analyzes classical cobordism spectra such as MO, MSO, MU.

Abstract

In this paper we analyze the higher topological Hochschild homology of commutative Thom S-algebras. This includes the case of the classical cobordism spectra MO, MSO, MU, etc. We consider the homotopy orbits of the torus action on iterated topological Hochschild homology and we describe the relationship to topological Andre-Quillen homology.