Geodesic
Coxeter systems with 2–dimensional Davis complexes, growth rates and Perron numbers
Bredon, Naomi1 ; Yukita, Tomoshige2
1 Department of Mathematics, University of Fribourg, Fribourg, Switzerland
2 Department of Mathematics, School of Education, Waseda University, Tokyo, Japan
Algebraic and Geometric Topology, Tome 24 (2024) no. 3, pp. 1787-1808

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2024.24.1787
Keywords: Coxeter systems, Davis complex, growth rates, Perron numbers

Bredon, Naomi 1 ; Yukita, Tomoshige 2

1 Department of Mathematics, University of Fribourg, Fribourg, Switzerland
2 Department of Mathematics, School of Education, Waseda University, Tokyo, Japan 
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Bredon, Naomi; Yukita, Tomoshige. Coxeter systems with 2–dimensional Davis complexes, growth rates and Perron numbers. Algebraic and Geometric Topology, Tome 24 (2024) no. 3, pp. 1787-1808. doi: 10.2140/agt.2024.24.1787

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