论文标题
关于Coxeter系统空间上增长率的连续性
On the continuity of the growth rate on the space of Coxeter systems
论文作者
论文摘要
弗洛伊德（Floyd）表明，如果一系列紧凑的双曲线多边形多边形会收敛，那么与多边形相关的coxeter基团生长速率的序列也是如此。对于双曲线3空间的情况，科尔帕科夫（Kolpakov）发现了相同的现象，用于特异性螺旋螺旋序列的聚合物的特定收敛序列。在本文中，我们表明增长率是Coxeter系统空间的连续函数。这是由于弗洛伊德（Floyd）和科尔帕科夫（Kolpakov）而引起的结果的扩展，因为在标记组的空间中，coxeter polyhedra的收敛序列产生了Coxeter系统的收敛序列。
Floyd showed that if a sequence of compact hyperbolic Coxeter polygons converges, then so does the sequence of the growth rates of the Coxeter groups associated with the polygons. For the case of the hyperbolic 3-space, Kolpakov discovered the same phenomena for specific convergent sequences of hyperbolic Coxeter polyhedra. In this paper, we show that the growth rate is a continuous function on the space of Coxeter systems. This is an extension of the results due to Floyd and Kolpakov since the convergent sequences of Coxeter polyhedra give rise to that of Coxeter systems in the space of marked groups.
