Topological Field Theory and Related Geometry

本文在共形场论、场理论、有限型拓扑不变量、曲面模空间和周期积分理论方面取得了以下进展。J. Murakami与T. Ohtsuki等人合作构造了3流形的泛有限型不变量。此外，我们还发现了这种有限型不变量与组形空间的环空间的上同调之间的关系。S. Morita主要从拓扑学的角度研究紧化黎曼曲面的模空间的几何以及映射类曲面群的结构，并在Torelli群上建立了重要的结果。Y. Shimizu在高属黎曼曲面的共形场论中发现了对射影平坦连接的明确描述。齐藤所提出的椭圆根系理论，为与拓扑场论有关的原始积分的研究开辟了新的思路。

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.