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

二十世纪数学的一个主要主题是群论与几何和拓扑学之间的深层联系。这种联系始于庞加莱对空间基本群概念的发现。这种联系最有趣的方面之一是群论和曲率之间的关系，特别是非正曲率。20世纪80年代的S在这最后一个领域看到了新的思想的涌入，包括以下几个方面：(1)研究“字双曲群”，即包含所有能在负曲线空间上适当地和余紧地作用的群；(2)对这种群的算法性质的认识导致了“自动群”概念的引入，(3)作用于树和R-树上的群的研究；(4)非正曲率多面体和二面体的研究及其在群的复形中的应用；(5)字双曲群的Novikov猜想和非正弯曲流形的拓扑刚性的研究。这个项目将支持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参观者，以及将于1992年6月第一周举行的一次会议。

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.