Witten Genus and Elliptic genera for proper actions

Abstract

In this paper, we construct for the first time, the Witten genus and elliptic genera on noncompact manifolds with a proper cocompact action by an almost connected Lie group and prove vanishing and rigidity results that generalise known results for compact group actions on compact manifolds. We also compute our genera for some interesting examples. We add an appendix on the equivariant non-spin case.