Mathematical Sciences: Geometric Group Theory and Topology

数学科学：几何群论和拓扑

• 批准号: 8701419
• 负责人: William Floyd
• 金额: $ 3.7万
• 依托单位: Virginia Polytechnic Institute and State University
• 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: 1987-06-15 至 1989-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701419&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Group; Theory

This program is mainly a study of invariants of not only the entire class of growth functions of a finitely generated group but also particular growth functions within that class. The goals are to extend the class of groups whose growth functions are known to be always rational, and to study further the growth functions that can occur for geometric groups. The attempt to show that rationality of the growth functions is independent of the generating set will be in the spirit of Cannon's work. The study of the growth functions that occur will continue the work of Floyd and Plotnick on planar groups. Special attention will be paid to reciprocity of the growth functions and to when the value at 1 is the reciprocal of the Euler characteristic. Many surprising and easily stated facts about geometric groups have been uncovered empirically, and it is time to bring some order into the area.

这个程序主要是研究有限生成群的整个增长函数类的不变量，以及该类中特定增长函数的不变量。我们的目标是扩展已知增长函数总是有理的群的类别，并进一步研究几何群可以出现的增长函数。试图证明增长函数的合理性与发电机组无关，这将是坎农工作的精神所在。对增长函数的研究将继续Floyd和Plotnick关于平面群的工作。将特别注意增长函数的倒数，以及当1处的值是欧拉特性的倒数时。关于几何群的许多令人惊讶和容易陈述的事实已经被经验地揭示出来，是时候给这个领域带来一些秩序了。