Rigidity and Vanishing Theorems on ${\mathbb{Z}}/k$ Spin$^c$ manifolds
Differential Geometry
2011-04-21 v1 Mathematical Physics
math.MP
Abstract
In this paper, we first establish an -equivariant index theorem for Spin Dirac operators on manifolds, then combining with the methods developed by Taubes \cite{MR998662} and Liu-Ma-Zhang \cite{MR1870666,MR2016198}, we extend Witten's rigidity theorem to the case of Spin manifolds. Among others, our results resolve a conjecture of Devoto \cite{MR1405063}
Cite
@article{arxiv.1104.3972,
title = {Rigidity and Vanishing Theorems on ${\mathbb{Z}}/k$ Spin$^c$ manifolds},
author = {Bo Liu and Jianqing Yu},
journal= {arXiv preprint arXiv:1104.3972},
year = {2011}
}