English

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 S1S^1-equivariant index theorem for Spinc^c Dirac operators on Z/k\mathbb{Z}/k 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 Z/k\mathbb{Z}/k Spinc^c manifolds. Among others, our results resolve a conjecture of Devoto \cite{MR1405063}

Keywords

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}
}
R2 v1 2026-06-21T17:56:42.028Z