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Arzhantseva, Goulnara; Niblo, Graham A.; Wright, Nick; Zhang, Jiawen

A characterization for asymptotic dimension growth. (English) Zbl 1481.20143

Algebr. Geom. Topol. 18, No. 1, 493-524 (2018).
Summary: We give a characterization for asymptotic dimension growth. We apply it to CAT(0) cube complexes of finite dimension, giving an alternative proof of Wright’s result on their finite asymptotic dimension. We also apply our new characterization to geodesic coarse median spaces of finite rank and establish that they have subexponential asymptotic dimension growth. This strengthens a recent result of J. Špakula and N. Wright [Algebr. Geom. Topol. 17, No. 4, 2481–2498 (2017; Zbl 1439.20048)].

Cited in 3 Documents

MSC:

20F65 Geometric group theory
20F67 Hyperbolic groups and nonpositively curved groups
20F69 Asymptotic properties of groups
51F99 Metric geometry

Keywords:

asymptotic dimension growth; CAT(0) cube complex; coarse median space; mapping class group

Citations:

Zbl 1439.20048
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Full Text: DOI arXiv Link

References:

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