A new upper bound for the Asymptotic Dimension of RACGs

Pub Date : 2023-10-04 DOI:10.4153/s0008439523000760
Panagiotis Tselekidis
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Abstract

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 $\mathrm{dim}_{CC}(\Gamma )$ , the clique-connected dimension of the graph. We generalize this result to graph products of finite groups.
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racg的渐近维数的一个新的上界
摘要设$W_{\Gamma} $是定义图$\Gamma $的直角Coxeter群。我们证明了$W_{\Gamma} $的渐近维数小于等于图的团连通维数$\ mathm {dim}_{CC}(\Gamma)$。我们把这个结果推广到有限群的图积。
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