$L^2$-index formula for proper cocompact group actions

Abstract

We study the index of the $G$-invariant elliptic pseudo-differential operator acting on a complete Riemannian manifold, where a unimodular, locally compact group $G$ acts properly and cocompactly. An $L^2$-index formula was obtained using the heat kernel method.

This is the final version (34 pages)

References in corpus (1)

• Connes-Chern character for manifolds with boundary and eta cochains

Cited by in corpus (2)

• Heat kernel estimates for the $\bar{\partial }$-Neumann problem on $G$-manifolds
• Localized Index and $L^2$-Lefschetz fixed point formula for orbifolds