Mathematical Sciences: Combinatorial Group Theory

数学科学：组合群论

• 批准号: 8821749
• 负责人: Stephen Gersten
• 金额: $ 6.45万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8821749&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Combinatorial; Group; Theory

This project will study groups through curvature conditions on simplicial complexes with these groups as their fundamental groups. A generalization of small cancellation theory is given and it is proposed to study these small cancellation groups and their finitely presented subgroups by curvature conditions. Higher dimensional analogues are proposed with applications to classes of groups traditionally studied by geometric methods. A group is an algebraic object having a binary operation defined on it. Such objects are of interest to many different branches of mathematics and physics. This project will study these groups by geometric methods.

这个项目将通过曲率来研究群体 条件单纯复形与这些群体作为他们的 基本群体。小相消的推广 理论，并建议研究这些小 消去群及其表示子群 曲率条件。提出了高维类似物 应用到传统上研究的群体类别， 几何方法 群是具有二元运算的代数对象 这样的对象是许多不同的人感兴趣的。 数学和物理学的分支。该项目将研究 这些组的几何方法。