Geodesic
On the continuity of the growth rate on the space of Coxeter systems
Tomoshige Yukita1 orcid
1Waseda University, Tokyo, Japan
Groups, geometry, and dynamics, Tome 18 (2024) no. 1, pp. 109-126

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DOI

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.
DOI : 10.4171/ggd/741
Classification : 20-XX
Mots-clés : Coxeter group, growth rate, space of marked groups, exponential growth

Tomoshige Yukita  1

1 Waseda University, Tokyo, Japan 
Tomoshige Yukita. On the continuity of the growth rate on the space of Coxeter systems. Groups, geometry, and dynamics, Tome 18 (2024) no. 1, pp. 109-126. doi: 10.4171/ggd/741
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