On The Witten Rigidity Theorem For String~C Manifolds

Elliptic genera were discovered in the mid1980’s in the work of Landweber-Stong [7], Ochanine [16] and Witten [18,19]. To date elliptic genera continue to be studied and have played important roles in many subjects of mathematics and theoretical physics.This paper focus on the Witten rigidity theorem on Stringc manifolds. We establish the family rigidity and vanishing theorems on the equivariant K-theory level for the Witten type operators on Stringc manifolds introduced by Chen-Han-Zhang [3]. Our approach follows closely the one used by Liu, Ma and Zhang [14,15] in the study of family rigidity, which is in inspired by the original proof of Witten rigidity theorem by Taubes [17].