The order of curvature operators on loop groups

TL;DR

This paper determines the precise order of the curvature operator on loop groups, depending on a Sobolev parameter, extending previous results by Freed and Maeda-Rosenberg-Torres.

Contribution

It provides an exact computation of the curvature operator order on loop groups, which was previously only estimated or partially known.

Findings

Exact order of the curvature operator depending on Sobolev parameter

Extension of previous results by Freed and Maeda-Rosenberg-Torres

Improved understanding of geometric operators on loop groups

Abstract

For loop groups (free and based), we compute the exact order of the curvature operator of the Levi-Civita connection depending on a Sobolev space parameter. This extends results of Freed and Maeda-Rosenberg-Torres.