Mathematical Sciences: A Research Quarter and Conference in Nonpositive Curvature and Geometric Group Theory; June 13- 16, 1992, Columbus, OH

20世纪数学的一个重要主题是群论与几何和拓扑学之间的深刻联系。这种联系始于庞加莱对空间基本群概念的发现。这种联系中最有趣的一个方面是群论与曲率，特别是非正曲率之间的关系。20世纪80年代，在最后一个领域出现了新的想法，包括：(1)研究“词双曲群”，即包含所有能在负弯曲空间上恰当且紧致作用的群的类；(2)对此类群的算法特征的认识，导致引入“自动群”的概念；(3)作用于树和r树的群的研究；(4)非正曲率多面体和圆面体的研究及其在群复上的应用；(5)字双曲群的Novikov猜想及非正弯曲流形的拓扑刚性研究。该项目将支持1992年春季在俄亥俄州立大学举行的非正曲率和几何群论研究季度。这项活动将包括长期和短期访问者，以及将于1992年6月第一个星期举行的一次会议。

A major theme of twentieth century mathematics has been the deep connections between group theory and geometry and topology. This connection began with Poincare's discovery of the notion of the fundamental group of a space. One of the most interesting aspects of this connection is the relationship between group theory and curvature in particular, nonpositive curvature. The 1980's saw a new influx of ideas in this last area including the following: (1) work on "word hyperbolic groups," that is, a class which contains all groups which can act properly and cocompactly on negatively curved spaces, (2) the recognition of the algorithmic character of such groups leading to the introduction of the notion of "automatic groups," (3) the study of groups acting on trees and R-trees, (4) work on polyhedra and orbihedra of nonpositive curvature and applications to complexes of groups, and (5) the Novikov conjecture for word hyperbolic groups and work on topological rigidity of nonpositively curved manifolds. This project will support a research quarter in Nonpositive Curvature and Geometric Group Theory to be held at the Ohio State University during the Spring Quarter of 1992. The activity will include both long and short term visitors, as well as a conference which will be held during the first week of June 1992.