String operations on rational Gorenstein spaces

Abstract

Félix and Thomas developed string topology of Chas and Sullivan on simply-connected Gorenstein spaces. In this paper, we prove that the degree shifted homology of the free loop space of a simply-connected $\mathbb{Q}$-Gorenstein space with rational coefficient is a non-unital and non-counital Frobenius algebra by solving the up to constant problem. We also investigate triviality or non-triviality of the loop product and coproduct of particular Gorenstein spaces.

27pages

References in corpus (2)

• A polarized view of string topology
• String topology of classifying spaces