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.

小组和分裂的几何这个项目有四个组成部分。第一部分需要研究群的高维填充不变量，重点是构建展示所有可能行为的例子。Forester和他的合作者Brady、Bridson和Shankar打算开发计算这些不变量的一般方法，并研究子群畸变和曲率的作用。第二个部分涉及特定类群（如极限群）的几何结构的构造，以及这些群的子群和端点的结构的研究。在第三部分，Forester将研究广义Baumslag-Solitar群的分类和应用。在第四部分中，Forester将继续他与Rourke在无扭转群情况下的多变量附加问题上的工作。这项工作扩展和发展了Klyachko的方法。群论是关于对称性的理论，在数学中起着基础性的作用。对称（或“群”）的概念很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，人们通过构建为手头的群量身定制的几何空间来研究抽象群，以便“看到”对称性并理解它。该项目涉及对由此构建的几何空间的详细研究。