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

本研究的主要成果有以下三个方面。我们对有关环面束和沿纤维微扰的局部指数理论的表述进行了实质性的修改。我们还对其在哈密顿环面作用的量化猜想的几何证明中的应用进行了修正。这两篇论文都被Comm. Math接受。物理. .2. 我们计算了由测地线流在标准球的共切束上产生的局部指数。在计算中，我们使用了协切束的紧化描述和局部指标在辛切下的行为。3. 给出了一类圆等变指标的公式。我们研究了Braverman， Ma-Zhang的等变指数理论与横向指数理论的异同，并就此写了一篇论文。

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.