Chern-Weil theory for certain infinite-dimensional Lie groups

TL;DR

This paper explores the extension of Chern-Weil and Chern-Simons theories to infinite-dimensional Lie groups, using invariant theory to identify cohomology classes in spaces of maps and diffeomorphism groups.

Contribution

It introduces methods to analyze the invariant theory of certain infinite-dimensional Lie groups and applies these techniques to detect cohomology classes in geometric and physical contexts.

Findings

Extension of Chern-Weil theory to infinite-dimensional groups

Detection of cohomology classes in mapping spaces

Application to diffeomorphism groups

Abstract

Chern-Weil and Chern-Simons theory extend to certain infinite-rank bundles that appear in mathematical physics. We discuss what is known of the invariant theory of the corresponding infinite-dimensional Lie groups. We use these techniques to detect cohomology classes for spaces of maps between manifolds and for diffeomorphism groups of manifolds.