Mathematical Sciences: Geometric Group Theory

数学科学：几何群论

• 批准号: 9200433
• 负责人: Stephen Gersten
• 金额: $ 17.35万
• 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: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9200433&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Group; Theory

This award supports research in geometric group theory. The central theme is to consider a finitely generated group as a geometric object through its Cayley graph. The principal investigator will study (bi)-automatic groups and (bi)-combable groups; isodiametric and isoperimetric inequalities; and free group automorphisms. 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 theme 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研究。 中心主题是通过凯莱图将有限生成群视为几何对象。 主要研究者将研究(bi)-自动组和(bi)-可梳理组；等径和等周不等式；和自由群自同构。 群是一个代数对象，其上定义了乘法。 组可以具有无限数量的元素或有限数量的元素。 在无限群的情况下，通常通过将它们与某种类型的有限对象相关联来研究它们。 就该奖项而言，中心主题是通过凯莱图将有限生成群视为几何对象。 这项工作与数学以及计算机科学的多个领域都有联系。