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Torus Fibrations and Localization of Index III

Equivariant Version and Its Applications

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Abstract

This paper is the third of the series concerning the localization of the index of Dirac-type operators. In our previous papers we gave a formulation of index of Dirac-type operators on open manifolds under some geometric setting, whose typical example was given by the structure of a torus fiber bundle on the ends of the open manifolds. We introduce two equivariant versions of the localization. As an application, we give a proof of Guillemin-Sternberg’s quantization conjecture in the case of torus action.

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Authors and Affiliations

  1. Department of Mathematical and Physical Sciences, Japan Women’s University, 2-8-1 Mejirodai, Bunkyo-ku, Tokyo, 112-8681, Japan

    Hajime Fujita

  2. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan

    Mikio Furuta

  3. Department of Mathematics, School of Science and Technology, Meiji University, 1-1-1 Higashimita, Tama-ku, Kawasaki, 214-8571, Japan

    Takahiko Yoshida

Authors
  1. Hajime Fujita
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  2. Mikio Furuta
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  3. Takahiko Yoshida
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Correspondence to Takahiko Yoshida.

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Communicated by A. Connes

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Fujita, H., Furuta, M. & Yoshida, T. Torus Fibrations and Localization of Index III. Commun. Math. Phys. 327, 665–689 (2014). https://doi.org/10.1007/s00220-014-2039-4

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  • DOI: https://doi.org/10.1007/s00220-014-2039-4

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