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In this paper, we first establish an S-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].

Rigidity and vanishing theorems on ℤ/𝕜 Spin^{𝕔} manifolds