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Cyclic actions and elliptic genera

Anand Dessai
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Abstract

Let $M$ be a $Spin$-manifold with $S^1$-action and let $σ\in S^1$ be of finite order. We show that the indices of certain twisted Dirac operators vanish if the action of $σ$ has sufficiently large fixed point codimension. These indices occur in the Fourier expansion of the elliptic genus of $M$ in one of its cusps. As a by-product we obtain a new proof of a theorem of Hirzebruch and Slodowy on involutions.

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Anand Dessai. 2002-03-20. Cyclic actions and elliptic genera. https://arxiv.org/abs/math/0104255

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