中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

华罗庚数学讲座

报告人：Prof. F. T. Farrell（Department of Mathematical Sciences Binghamton University）

题  目：Negative curvature from a topological perspective

时  间：11.30(星期一), 15：00-17：00 (14：30-15：00为茶点时间, 地点: 思源楼509房间)

地  点：晨兴中心110房间

Abstract：

I will report on work due to many people including some joint work with L.E.Jones, P.Ontaneda, and M. S. Raghunathan. Let M be a m-dimensional, closed (i.e. compact and with empty boundary) Riemannian manifold all of whose sectional curvatures are negative. Two classical results on the topology of such M are:
1.(Cartan-Hadamard) The universal cover of M is diffeomorphic to m-dimensional Euclidean space.

2.(Preissmann) Every abelian subgroup of the fundamental group of M is cyclic.
     I will report on recent progress on some further questions; e.g.
    A. To what extent does its fundamental group determine M?
    B. What can be said about the topology of the space of all negatively curved Riemannian metrics on M?

华罗庚数学讲座

常年不断举办的各种讨论班和学术讲座更显示出实验室的生机与活力，其中一年一度的“华罗庚讲座”，每次邀请两、三名国内外著名数学家作报告，享誉学术界，产生了广泛影响。