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arXiv · 2112.09440

A new upper bound for the Asymptotic Dimension of RACGs

Panagiotis Tselekidis
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Abstract

Let $W_\Gamma$ be the Right-Angled Coxeter group with defining graph $\Gamma$. We show that the asymptotic dimension of $W_\Gamma$ is smaller than or equal to $dim_{CC}(\Gamma)$, the clique-connected dimension of the graph. As a corollary we show that $W_\Gamma$ is virtually free if and only if $dim_{CC}(\Gamma)=1$.

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Panagiotis Tselekidis. 2021-12-17. A new upper bound for the Asymptotic Dimension of RACGs. https://doi.org/10.4153/s0008439523000760

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