On the string topology category of compact Lie groups

TL;DR

This paper applies stratification techniques to the string topology category of simply connected compact Lie groups, revealing new structural properties within this mathematical framework.

Contribution

It demonstrates that stratification methods can be effectively used to analyze the string topology category of simply connected compact Lie groups, a novel application in this context.

Findings

Stratification applies to the string topology category of simply connected compact Lie groups.

Derived properties of the string topology categories using stratification.

Enhanced understanding of the categorical structure of string topology in Lie groups.

Abstract

This paper examines the string topology category of a manifold, defined by Blumberg, Cohen and Teleman. Since the string topology category is a subcategory of a compactly generated triangulated category, the machinery of stratification, constructed by Benson, Krause and Iyengar, can be applied in order to gain an understanding of the string topology category. It is shown that an appropriate stratification holds when the manifold in question is a simply connected compact Lie group. This last result is used to derive some properties of the relevant string topology categories.