论文信息 - Bouquets Revisited and Equivariant Elliptic Cohomology

Bouquets Revisited and Equivariant Elliptic Cohomology

Let M be a spin manifold with a circular action. Given an elliptic curve E, we introduce, as in Grojnowski, elliptic bouquets of germs of holomorphic equivariant cohomology classes on M. Following Bott-Taubes and Rosu, we show that integration of an elliptic bouquet is well defined. In particular, this imply Witten's rigidity theorem. We emphasize the similarity between integration in K-theory and in elliptic cohomology.

M. Vergne

[1] Xiaoyang Chen,et al. A vanishing theorem for elliptic genera under a Ricci curvature bound , 2020 .

[2] Kefeng Liu,et al. Rigidity and vanishing theorems in $K$-theory , 1999, math/9912108.

[3] Ioanid Roşu. Equivariant elliptic cohomology and rigidity , 1999, math/9912089.

[4] Kefeng Liu,et al. On family rigidity theorems, I , 1999, math/9910047.

[5] Paul-Emile Paradan,et al. Formules de localisation en cohomologie equivariante , 1999, Compositio Mathematica.

[6] Michèle Vergne,et al. Heat Kernels and Dirac Operators: Grundlehren 298 , 1992 .

[7] M. Vergne,et al. The Equivariant Index and Kirillov's Character Formula , 1985 .

[8] Kefeng Liu. On modular invariance and rigidity theorems , 1995 .

[9] M. Vergne. Geometric Quantization and Equivariant Cohomology , 1994 .

[10] R. Bott,et al. On the rigidity theorems of Witten , 1989 .

[11] E. Witten. The index of the dirac operator in loop space , 1988 .