Transgressive loop group extensions

TL;DR

This paper characterizes transgressive loop group extensions, which relate to higher-dimensional cohomology classes, using loop fusion and thin homotopy concepts within finite-dimensional, higher-categorical geometry.

Contribution

It provides a loop-group theoretical characterization of transgressive central extensions through fusion and homotopy invariance, linking cohomology with geometric structures.

Findings

Transgressive extensions correspond to degree four cohomology classes.

Characterization via loop fusion and thin homotopy equivariance.

Framework connects higher cohomology with geometric loop group structures.

Abstract

A central extension of the loop group of a Lie group is called transgressive, if it corresponds under transgression to a degree four class in the cohomology of the classifying space of the Lie group. Transgressive loop group extensions are those that can be explored by finite-dimensional, higher-categorical geometry over the Lie group. We show how transgressive central extensions can be characterized in a loop-group theoretical way, in terms of loop fusion and thin homotopy equivariance.