Homology of E_n Ring Spectra and Iterated THH

TL;DR

This paper introduces an iterative construction of topological Hochschild homology (THH) for E_n ring spectra, linking it to the shifted cotangent complex and topological Quillen homology, advancing algebraic topology methods.

Contribution

It presents a novel iterative bar construction for THH of E_n ring spectra, providing a new model for the shifted cotangent complex and reduced topological Quillen homology.

Findings

Iterative bar construction for THH of E_n ring spectra.

Model for shifted cotangent complex at the augmentation.

Connection to reduced topological Quillen homology.

Abstract

We describe an iterable construction of THH for an E_n ring spectrum. The reduced version is an iterable bar construction and its n-th iterate gives a model for the shifted cotangent complex at the augmentation, representing reduced topological Quillen homology of an augmented E_n algebra.