Topological Field Theory and Related Geometry

拓扑场论及相关几何

• 批准号: 09304005
• 负责人: KOHNO Toshitake
• 金额: $ 7.1万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09304005/
• 关键词: conformal field theory; finite type invariants; loop space; configuration space; moduli space; Torelli group; 量子群; 点の配置の空間; チャーン・サイモンズ理論; バシリエフ不変量; カシャエフ予想; ジョーンズ多項式; 原始積分; 組みひも群; 写像類群; ウィッテン不変量; モノドロミー表現; 位相的場の理論; チャーン-サイモンズ摂動理論; ファインマ

We have made the following progress in conformal field theory, field theory, finite type topological invariants, moduli space of surfaces and the theory of period integrals. J. Murakami constructed a universal finite type invariant for 3-manifold in collaboration with T. Ohtsuki and others. Moreover, we discovered a relationship between such finite type invariants and the cohomology of the loop spaces of configuration spaces (T. Kohno). S. Morita investigated the geometry of the moduli space of compact Riemann surfaces as well as the structure of the mapping class group of surfaces mainly from the point of view of topology and established important results on the Torelli group. Y. Shimizu found an explecit description of the projectively flat connection for the conformal fieldtheory of Riemann surfaces of higher genera. The theory of elliptic root system due to K. Saito shead new lights on the study of primitive integrals in relation with topological field theory.

我们已经在保形场理论，现场理论，有限型拓扑，表面的模量和时期积分理论方面取得了以下进展。 J. Murakami与T. Ohtsuki和其他人合作，为3-Manifold构建了一种通用有限类型。此外，我们发现了这种有限类型不变的构造与配置空间环路的共同体之间的关系（T. Kohno）。莫里塔（S. Morita）研究了紧凑型riemann表面的模量空间的几何形状，以及主要是从拓扑的角度来看的表面映射类组的结构，并在托雷利（Torelli）组上确立了重要的结果。 Y. Shimizu发现了对较高属的Riemann表面的共形野外理论的公平连接的解释说明。 K. saito在研究原始积分与拓扑场理论有关的研究中，椭圆形根系统的理论。

项目成果

河野俊丈: "Chern-Simons perturbative invariants" Lactures at Knots′96 Series on Knots and Everything. 15. 235-262 (1997)

Toshitake Kono：“Chern-Simons 微扰不变量”在 Knots96 系列上关于 Knots 和 Everything 的演讲 15. 235-262 (1997)。

Toshitake Kohno and Toshie Takata: "Level-rank duality of Witten's 3-manifold invasias" Advanced Studies in Pure Math.24. 243-264 (1996)

Toshitake Kohno 和 Toshie Takata：“Witten 3 流形入侵的等级对偶性”纯数学高级研究.24。

森田茂之(河澄響矢と共著): "The primary approximation to the cohomology of the moduli spa ce of curves and coaycles for the stable class" Math.Reseanch Letters. 3. 629-641 (1996)

Shigeyuki Morita（与 Kyoya Kawasumi 合着）：“稳定类的曲线和 coaycles 模空间的上同调的主要近似”Math.Resench Letters 3. 629-641 (1996)。

Shigeyuki Morita: "Structure of the mapping class groups of surfaces: a survey and a prospect"Geometry and Topology Monographs. 2. 349-406 (1999)

森田繁之：《曲面映射类群的结构：综述与展望》几何与拓扑学专着。

河野俊丈,高田敏恵: "Level-rank duality of Witten′s 3-manibold invariants" Advanced Studies in Pure Marh.24. 243-264 (1996)

Toshitake Kono、Toshie Takada：“Witten 3-manibold 不变量的等级对偶性”Advanced Studies in Pure Marh.243-264 (1996)。