Topological coHochschild Homology and the Homology of Free Loop Spaces

TL;DR

This paper develops new topological and algebraic methods based on topological coHochschild homology to compute the homology of free loop spaces, extending previous results in the field.

Contribution

It introduces novel spectrum-level structures and spectral sequence techniques for coTHH, enabling new calculations of free loop space homology.

Findings

Computed homology of free loop spaces in new cases

Developed spectrum-level structures for coTHH

Enhanced algebraic tools for spectral sequence analysis

Abstract

We study the homology of free loop spaces via techniques arising from the theory of topological coHochschild homology (coTHH). Topological coHochschild homology is a topological analogue of the classical theory of coHochschild homology for coalgebras. We produce new spectrum-level structure on coTHH of suspension spectra as well as new algebraic structure in the coB\"okstedt spectral sequence for computing coTHH. These new techniques allow us to compute the homology of free loop spaces in several new cases, extending known calculations.