Mathematical Sciences: Geometric Group Theory

数学科学：几何群论

• 批准号: 9500769
• 负责人: Stephen Gersten
• 金额: $ 15.06万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500769&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Group; Theory

This award supports work in geometric group theory. The principal investigator will continue to study groups as geometric objects and to extend these ideas to handle geometric questions involving pairs consisting of a group and a subgroup. In particular, he will determine the structure of finitely presented subgroups of a hyperbolic group. He will also study the quasi-isometry types of various groups. A group is an algebraic object having a multiplication defined on it. Groups can have an infinite number of elements or a finite number of elements. In the case of infinite groups, they are often studied by associating with them finite objects of some type. In the case of this award, the central them has been to consider a finitely generated group as a geometric object through its Cayley graph. This work has connections to several areas of mathematics, as well as computer science.

该奖项支持几何群论的工作。 主要研究者将继续研究组的几何对象，并扩展这些想法来处理几何问题，涉及对组成的一个组和一个子组。 特别是，他将确定的结构，提出的子群的双曲群。 他还将研究各种群体的准等距类型。 一个群是一个代数对象，在它上面定义了乘法。群可以有无限个元素，也可以有有限个元素。 在无限群的情况下，它们通常通过与某种类型的有限对象相关联来研究。 在这个奖项的情况下，他们的中心一直认为一个candergenerated组作为一个几何对象，通过其凯莱图。 这项工作与数学的几个领域以及计算机科学有关。