Description and triviality of the loop products and coproducts for rational Gorenstein spaces

TL;DR

This paper explicitly describes loop products and coproducts for rational Gorenstein spaces using Sullivan models and investigates conditions under which these operations are trivial, extending previous results in the field.

Contribution

It provides explicit Sullivan model descriptions of loop operations and establishes new triviality results, generalizing prior work by Tamanoi, Félix, Thomas, and Naito.

Findings

Explicit Sullivan model descriptions of loop operations

Conditions for triviality of loop products and coproducts

Generalizations of existing triviality results

Abstract

F\'elix and Thomas extended the loop products and coproducts to simply-connected Gorenstein spaces. We explicitly describe these operations with rational coefficients in terms of Sullivan models. Moreover, by this description, we prove some results on triviality of these operations. They include a variant of the result of Tamanoi, and generalizations of that of F\'elix and Thomas and that of Naito.