Localization of Riemann-Roch number via torus bundles and its application

点击翻译按钮获取中文摘要

Main results of this research are the following three.1. We substantially revised the paper concerning a formulation of local index theory via torus bundles and a perturbation along the fibers. We also revised the paper concerning its application to a geometric proof of the quantization conjecture for Hamiltonian torus action. Both papers are accepted to Comm. Math. Phys.. 2. We computed the local index arising from the geodesic flow on the cotangent bundle of the standard sphere. In the computation we used the description of a compactification of the cotangent bundle and behavior of the local index under the symplectic cutting. 3. We gave a formulation of a kind of circle equivariant index. We investigated difference and similarity between our equivariant index and the theory of transverse index due to Braverman, Ma-Zhang, and we wrote a paper on the subject.