Singular equivariant asymptotics and the moment map I

TL;DR

This paper investigates the asymptotic behavior of integrals related to the spectrum of invariant elliptic operators on manifolds with Lie group actions, utilizing the moment map in equivariant cohomology.

Contribution

It introduces a novel approach to analyze asymptotics in the context of equivariant geometry and spectral theory involving Lie group symmetries.

Findings

Asymptotic formulas for integrals associated with invariant elliptic operators.

Connections established between spectral properties and equivariant cohomology.

Foundational results for subsequent papers in the series.

Abstract

This is the first of a series of papers dealing with the asymptotic behavior of certain integrals occuring in the description of the spectrum of an invariant elliptic operator on a compact Riemannian manifold carrying the action of a compact, connected Lie group of isometries, and in the study of its equivariant cohomology via the moment map.