Growth rates and spectral radii of Coxeter groups

Abstract: The growth rate $\omega(G,S)$ and spectral radius $\lambda_{(\Gamma,S)}$ of a finitely generated group $(\Gamma,S)$ is a quantity related to the Cayley graph $\text{Cay}(\Gamma,S)$ that measure complexity of $\text{Cay}(\Gamma,S)$. In this talk, we focus on Coxeter groups which are generalizations of reflection groups. First, we consider the space $\mathcal{C}$ of Coxeter groups which is the subspace in the space of marked groups consisting of Coxeter systems, and show that $\mathcal{C}$ is compact. Second, we prove that growth rates are continuous in $\mathcal{C}$ and provide examples of convergence and spectral radii of Coxeter groups.

group theory

Audience: researchers in the topic

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