群与单关系群图的渐近维数

IF 0.6 3区数学 Q3 MATHEMATICS

Algebraic and Geometric Topology Pub Date : 2023-11-05 DOI:10.2140/agt.2023.23.3587

Panagiotis Tselekidis

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引用次数: 4

摘要

我们证明了hnn扩展的渐近维数的一个新的不等式。我们推导出每一个关联群的渐近维数最多为2，证实了a . dranishnikov的一个猜想。作为另一个推论，我们计算了直角Artin群的精确渐近维数。证明了群图的基本群的渐近维数的一个新的上界。这就得到了有限生成群的渐近Morita猜想的部分结果。

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Asymptotic dimension of graphs of groups and one-relator groups

We prove a new inequality for the asymptotic dimension of HNN-extensions. We deduce that the asymptotic dimension of every one relator group is at most two, confirming a conjecture of A.Dranishnikov. As another corollary we calculate the exact asymptotic dimension of Right-angled Artin groups. We prove a new upper bound for the asymptotic dimension of fundamental groups of graphs of groups. This leads to a partial result on the asymptotic Morita conjecture for finitely generated groups.

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