Several new Witten rigidity theorems for spin${}^c$ manifolds

Abstract

Using Liu's modular invariance method and its odd-dimensional extension by Han and Yu, we establish new Witten rigidity theorems for the generalized Witten genus of twisted Dirac operators on even-dimensional spin${}^c$ manifolds and twisted Toeplitz operators on odd-dimensional spin${}^c$ manifolds with circle actions.