A Local Index Theorem of Transversal Type on Manifolds with Locally Free ${\mathbb{S}}^1$-action

Dung-Cheng Lin, I-Hsun Tsai

We study an index of a transversal Dirac operator on an odd-dimensional manifold $X$ with locally free ${\mathbb{S}}^1$-action. One difficulty of using heat kernel method lies in the…