报告题目：Infinite Dimensional Manifolds from a New Point of View

报 告 人：林贤祖 博士（福建师范大学数学系）

报告时间：10月23日下午3 - 4点

报告地点：数学实验室

摘要：We propose a new treatment about infinite dimensional manifolds. Our treatment differs from the usual one in three respects. First, we adopt the language of categories and functors and our definition of infinite dimensional manifolds is a natural generalization of finite dimensional manifolds in the sense that de Rham cohomology and singular cohomology can be naturally defined and the basic properties (Functorial Property, Homotopy Invariant, Mayer-Vietoris Sequence) are preserved. Second, we need no topology except the topology of finite dimensional manifolds. Thus we would not talk about the topology of an infinite dimensional manifold, instead we still have the homotopy type of an infinite dimensional manifold. Finally we can naturally define many classes of infinite dimensional manifolds including space of smooth mappings between finite dimensional manifolds, group of diffeomorphisms of a finite dimensional manifold and classifying space of Lie group.

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注：本次讲座将纳入数学系继续教育课程。

理学院

2017年10月20日