Several new Witten rigidity theorems for elliptic genus

Abstract

Using the Liu's method, we prove a new Witten rigidity theorem of elliptic genus of twisted Dirac operators in even dimensional spin manifolds under the circle action. Combined with the Han-Yu's method, we prove the Witten rigidity theorems of elliptic genus of twisted Toplitz operators of odd-dimensional spin manifolds under the circle action. Moreover, we have obtained several similar Witten rigidity theorems of elliptic genus.

arXiv admin note: text overlap with arXiv:2401.06944. text overlap with arXiv:1504.03007 by other authors