Mathematical Sciences: Geometric Group Theory and Topology

这个程序主要是一个不变量的研究，不仅 n-生成群的增长函数的整类 而且在这一类中也有特殊的生长功能。 的 目标是扩展其增长函数 都知道总是理性的，并进一步研究增长， 函数可以发生几何组。 的尝试 表明增长函数的合理性与 发电机组将秉承坎农的精神 的 对发生的增长函数的研究将继续进行 弗洛伊德和普罗特尼克关于平面群的研究。 将特别注意 增长函数的互易性以及 值为1是欧拉特征线的倒数。 许多 关于几何群的令人惊讶且易于陈述的事实， 已经被经验发现，现在是时候带来一些秩序 进入该地区。

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.