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- W4387459402 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." @default.
- W4387459402 created "2023-10-10" @default.
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- W4387459402 date "2020-11-19" @default.
- W4387459402 modified "2023-10-11" @default.
- W4387459402 title "On the continuity of the growth rate on the space of Coxeter systems" @default.
- W4387459402 doi "https://doi.org/10.48550/arxiv.2011.09953" @default.
- W4387459402 hasPublicationYear "2020" @default.
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