Primary and secondary invariants of Dirac operators on $G$-proper manifolds

TL;DR

This paper surveys recent methods for constructing cyclic cocycles on the Harish-Chandra Schwartz algebra of real reductive Lie groups and explores their applications in higher index theory for proper cocompact group actions.

Contribution

It introduces new constructions of cyclic cocycles and applies them to advance higher index theory on $G$-proper manifolds.

Findings

New cyclic cocycle constructions for Harish-Chandra Schwartz algebra

Applications to higher index theory for proper cocompact $G$-actions

Enhanced understanding of Dirac operators on $G$-proper manifolds

Abstract

In this article, we survey the recent constructions of cyclic cocycles on the Harish-Chandra Schwartz algebra of a connected real reductive Lie group $G$ and their applications to higher index theory for proper cocompact $G$-actions.