Rigidity And Vanishing Theorems On Z/K Spin~C Manifolds

In this paper, we first establish an S1-equivariant index theorem for Spinc Dirac operators on Z/k manifolds, then combining with the methods developed by Taubes [24] and Liu-Ma-Zhang [19,20], we extend Witten’s rigidity theorem to the case of Z/k Spinc manifolds. Among others, our results resolve a conjecture of Devoto [6] in1996.