Mathematical Sciences: Algebraic Problems Arising Out of Cohomology of Groups, Fixed point Theory and Shape

数学科学：群上同调、不动点理论和形状引起的代数问题

• 批准号: 8703260
• 负责人: Ross Geoghegan
• 金额: $ 5.45万
• 依托单位: SUNY at Albany
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1990-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8703260&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algebraic; Problems; Arising

Professor Geoghegan's areas of interest are topology and related group theory. He will investigate problems in geometric and homological group theory for which topological methods, coming from shape theory, fixed point theory and infinite- dimensional topology, are appropriate. More specifically he will investigate various questions involving finiteness properties and cohomological properties of groups which can be interpreted as questions about "ends" of covering spaces. He will continue his collaboration with Professor K.S. Brown of Cornell University on infinite-dimensional finitely presented discrete groups. On his own he will continue his investigation of the topological meaning of a well known conjecture of H. Bass about the Hattori-Stallings trace of an idempotent matrix with group ring entries. Groups are ubiquitous in mathematics and the natural sciences as codifiers of symmetry, and one can never have too many approaches to discovering their properties.

Geoghegan教授的兴趣领域是拓扑学和 相关群体理论 他将研究几何问题 和同调群理论，拓扑方法， 来自形状理论，不动点理论和无限- 三维拓扑结构是合适的。 更具体地说，他将 研究涉及有限性性质的各种问题， 群的上同调性质可以解释为 关于覆盖空间的“端点”的问题。 他将继续他的 与K.S.教授合作康奈尔大学的布朗在 无限维有限表示的离散群。 在他 他将继续他的拓扑意义的调查 一个著名的H.关于Hattori-Stallings 具有群环元素的幂等矩阵的迹。 组 在数学和自然科学中无处不在， 对称性的编码器，人们永远不会有太多的方法 发现它们的特性