Geometry of Groups and Splittings

组和分裂的几何

基本信息

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

项目摘要

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.

组和分裂的几何形状这个项目具有四个组成部分。第一个组成部分需要研究组的较高维度填充物的研究，重点是建立示例，展示了可能行为的全部范围。 Forester和合作者Brady，Bridson和Shankar打算开发用于计算此类不变性的一般方法，并研究亚组扭曲和曲率的作用。第二个组成部分是针对特定类别组（例如极限组）的几何结构的构建，以及对这些组的子组和末端的结构的研究。在第三个组件的林务中，将对广义的鲍姆斯拉格 - 塞塔尔群体和追求应用程序的分类进行分类。在第四个组件中，林务将继续与Rourke一起处理无扭转组的多变量邻接问题。这项工作扩展了Klyachko'smethods.group理论是对称理论，它起着基本作用的作用。对称性（或“组”）的概念非常自然地摄取，但在其他更抽象的区域中也出现。在几何群体理论的领域中，第一，通过构造手头量身定制的小组来研究摘要组，以便“查看”对称性并理解它。该项目涉及如此构建的几何空间的详细研究。