On Family Rigidity Theorems II. arXiv:math/9911035
Preprint, arXiv:math/9911035 [math.DG] (1999).
Summary: 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.
MSC:
| 14-XX | Algebraic geometry |
| 57Rxx | Differential topology |
| 91-XX | Game theory, economics, finance, and other social and behavioral sciences |
| 22E67 | Loop groups and related constructions, group-theoretic treatment |
| 58G10 | Index theory and related fixed-point theorems [See also 19K56, 46L80] (MSC1991) |
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