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

本研究的主要成果有以下三点.我们实质性地修改了关于制定当地指数理论通过环面束和扰动沿着纤维。我们还修改了关于其应用于哈密顿环面作用量量子化猜想的几何证明的文章。两篇论文都被《通信数学物理》杂志接受。2.我们计算了标准球面余切丛上测地线流的局部指数。在计算中，我们使用了余切丛的紧化和局部指数在辛切割下的行为的描述。3.给出了一类圆等变指标的一个公式。我们研究了我们的同变指数与Braverman，Ma-Zhang的横向指数理论之间的区别和相似之处，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.