On Family Rigidity Theorems II

Kefeng LIU; Xiaonan MA

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On Family Rigidity Theorems II

Kefeng LIU·Xiaonan MA

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Abstract

In LM, we proved a family version of the famous Witten rigidity theorems and several family vanishing theorems for elliptic genera. In this paper, we gerenalize our theorems LM in two directions. First we establish a family rigidity theorem for the Dirac operator on loop space twisted by general positive energy loop group representations. Second we prove a family rigidity theorem for spin^c-manifolds. Several vanishing theorems on both cases are also obtained.

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Kefeng LIU, Xiaonan MA. 1999-11-05. On Family Rigidity Theorems II. https://arxiv.org/abs/math/9911035

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