Coxeter systems with 2–dimensional Davis complexes, growth rates and Perron numbers

Bredon, Naomi; Yukita, Tomoshige

doi:10.2140/agt.2024.24.1787

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Coxeter systems with $2$–dimensional Davis complexes, growth rates and Perron numbers

Naomi Bredon and Tomoshige Yukita

Algebraic & Geometric Topology 24 (2024) 1787–1808

DOI: 10.2140/agt.2024.24.1787

Abstract

We study growth rates of Coxeter systems with Davis complexes of dimension at most $2$ . We show that if the Euler characteristic $χ$ of the nerve of a Coxeter system is vanishing (resp. positive), then its growth rate is a Salem (resp. Pisot) number. In this way, we extend results due to Floyd (1992) and Parry (1993). In the case where $χ$ is negative, we provide infinitely many nonhyperbolic Coxeter systems whose growth rates are Perron numbers.

Keywords

Coxeter systems, Davis complex, growth rates, Perron numbers

Mathematical Subject Classification

Primary: 20F55, 20F65

References

Publication

Received: 27 December 2022

Revised: 4 February 2023

Accepted: 27 February 2023

Published: 28 June 2024

Authors

Naomi Bredon
Department of Mathematics University of Fribourg Fribourg Switzerland

Tomoshige Yukita
Department of Mathematics School of Education Waseda University Tokyo Japan

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Volume 24, issue 3 (2024)