Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 418

On Family Rigidity Theorems I

Kefeng Liu and Xiaonan Ma

Duke Math. J, to appear

In this paper, we first prove a local family version of the Atiyah-Bott-Segal-Singer Lefschetz fixed point formula, then we extend the famous Witten's rigidity Theorems to the family case. Several family vanishing theorems for elliptic genera are also proved.

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