On the continuity of the growth rate on the space of Coxeter systems

  • Tomoshige Yukita

    Waseda University, Tokyo, Japan
On the continuity of the growth rate on the space of Coxeter systems cover
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Abstract

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.

Cite this article

Tomoshige Yukita, On the continuity of the growth rate on the space of Coxeter systems. Groups Geom. Dyn. 18 (2024), no. 1, pp. 109–126

DOI 10.4171/GGD/741