In this paper we give a proof of the Lefschetz fixed point formula of Freed for an orientation-reversing involution on an odd dimensional spin manifold by using the direct geometric method introduced by Lafferty et al...In this paper we give a proof of the Lefschetz fixed point formula of Freed for an orientation-reversing involution on an odd dimensional spin manifold by using the direct geometric method introduced by Lafferty et al. And then we generalize this formula under the noncommutative geometry framework.展开更多
In this paper, we prove a local odd dimensional equivariant family index theorem which generalizes Freed＇s odd dimensional index formula. Then we extend this theorem to the noncommuta- tive geometry framework. As a c...In this paper, we prove a local odd dimensional equivariant family index theorem which generalizes Freed＇s odd dimensional index formula. Then we extend this theorem to the noncommuta- tive geometry framework. As a corollary, we get the odd family Lichnerowicz vanishing theorem and the odd family Atiyah-Hirzebruch vanishing theorem.展开更多
文摘In this paper we give a proof of the Lefschetz fixed point formula of Freed for an orientation-reversing involution on an odd dimensional spin manifold by using the direct geometric method introduced by Lafferty et al. And then we generalize this formula under the noncommutative geometry framework.
基金Supported by National Natural Science Foundation of China(Grant No.11271062)Program for New Century Excellent Talents in University(Grant No.13-0721)
文摘In this paper, we prove a local odd dimensional equivariant family index theorem which generalizes Freed＇s odd dimensional index formula. Then we extend this theorem to the noncommuta- tive geometry framework. As a corollary, we get the odd family Lichnerowicz vanishing theorem and the odd family Atiyah-Hirzebruch vanishing theorem.
