Deepening and application to integrable systems of index theory via perturbation of Dirac operator

2017 Fiscal Year Final Research Report

• Project/Area Number: 26800045
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Japan Women's University
• Principal Investigator: Fujita Hajime 日本女子大学, 理学部, 准教授 (50512159)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: Dirac作用素 / 同変指数 / 指数の局所化 / トーリック多様体 / 特異ファイバー / Origami多様体 / Delzant多面体 / 幾何学的量子化

Outline of Final Research Achievements

The results in this research are followings. 1. We defined the natural notion of cobordism in index theory via perturbation by Dirac operators along fibers, and we showed cobordism invariance of our index. 2. We gave a geometric proof of localization of equivariant Riemann-Roch number of toric origami manifolds. 3. We revised a paper about an S1-equivariant index of non-compact symplectic manifold with Hamiltonian S1-action. We also studied a localization of index in recent development of loop group equivariant index theory.

Free Research Field

幾何学(シンプレクティック幾何学、指数理論)