Geometry of Groups and Splittings

组和分裂的几何

• 批准号: 0605137
• 负责人: Max Forester
• 金额: $ 9.66万
• 依托单位: University of Oklahoma Norman Campus
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0605137&HistoricalAwards=false
• 关键词: Geometry; Groups; Splittings

Geometry of Groups and SplittingsThis project has four components. The first component entails the studyof higher dimensional filling invariants of groups, with emphasis oncontructing examples exhibiting the full range of possiblebehavior. Forester and collaborators Brady, Bridson, and Shankar intendto develop general methods for computing such invariants, and to studythe role of subgroup distortion and curvature. The second componentconcerns the construction of geometric structures for particular classesof groups, such as limit groups, and the study of the structure ofsubgroups and ends for these groups. In the third component Forester willinvestigate the classification of generalized Baumslag-Solitar groupsand pursue applications. In the fourth component Forester will continuehis work with Rourke on the multivariable adjunction problem, in the caseof torsion-free groups. This work extends and devolops Klyachko'smethods.Group theory is the theory of symmetry, which plays a fundamental role inmathematics. Notions of symmetry (or "groups") arise very naturally ingeometry, but also in other, more abstract, areas. In the field ofgeometric group theory one studies abstract groups by constructinggeometric spaces, tailor-made for the groups at hand, in order to "see"the symmetry and understand it. This project involves the detailed studyof the geometric spaces thus constructed.

几何群体和分裂这个项目有四个组成部分。第一个部分需要研究更高维度的填充不变量的群体，重点是构建展示全方位可能行为的例子。福雷斯特和他的合作者布雷迪、布赖森和尚卡尔打算发展计算这种不变量的一般方法，并研究子群畸变和曲率的作用。第二部分涉及特定类别的群的几何结构的构造，如极限群，以及研究这些群的子群和端点的结构。在第三部分中，Forester将研究广义Baumslag-Solitar群的分类并寻求应用。在第四个组成部分福雷斯特将继续他的工作与鲁尔克的多变量的附加问题，在案件的torsion-free团体。群论是对称性的理论，它在数学中起着基础性的作用。对称性（或“群”）的概念非常自然地出现在几何学中，但也出现在其他更抽象的领域。在几何群论领域，人们通过构造几何空间来研究抽象群，为手头的群量身定做，以便“看到“对称性并理解它。