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- W3102067145 abstract "Floyd showed that if a sequence of compact hyperbolic Coxeter polygons converges, then so do the growth rates of the Coxeter groups associated with the polygons. For the case of the hyperbolic 3-space, Kolpakov discovered the same phenomenon 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 groups. 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 groups in the space of marked groups." @default.
- W3102067145 created "2020-11-23" @default.
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- W3102067145 date "2020-11-19" @default.
- W3102067145 modified "2023-10-11" @default.
- W3102067145 title "On the continuity of the growth rate on the space of Coxeter groups" @default.
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