Primary and secondary invariants 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.

41 pages. In this new arXiv version we correct a mistake in the printed version by avoiding a wrong decomposition formula for the Dirac operator. A detailed discussion can be found in arXiv:2108.00982(v3)