A transverse Chern character for compact Lie group actions

TL;DR

This paper explores new perspectives on transverse index theory for compact Lie group actions, connecting Kasparov's work with classical results by Berline-Vergne and Paradan-Vergne.

Contribution

It introduces a transverse Chern character framework for analyzing compact Lie group actions on manifolds, building on Kasparov's recent developments.

Findings

Establishes a new transverse Chern character concept

Links Kasparov's index theory with classical localization formulas

Provides potential pathways for further research in equivariant index theory

Abstract

This article aims to explore new perspectives offered by Kasparov's recent work on transverse index theory in the context of actions of compact Lie groups on a manifold, and hints at potential connections to the work of Berline-Vergne and Paradan-Vergne.