Torus fibrations and localization of index III
arXiv:1008.5007 · doi:10.1007/s00220-014-2039-4
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.
24 pages. To appear in Comm. Math. Phys