A Comparison of Large Scale Dimension of a Metric Space to the Dimension of its Boundary

Craig R. Guilbault; Molly A. Moran

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arXiv · 1507.04395

A Comparison of Large Scale Dimension of a Metric Space to the Dimension of its Boundary

Craig R. Guilbault·Molly A. Moran

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Abstract

Buyalo and Lebedeva have shown that the asymptotic dimension of a hyperbolic group is equal to the dimension of the group boundary plus one. Among the work presented here is a partial extension of that result to all groups admitting $\mathcal{Z}$-structures; in particular, we show that $\hbox{asdim}G\geq \hbox{dim}Z+1$ where $Z$ is the $\mathcal{Z}$-boundary.

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Craig R. Guilbault, Molly A. Moran. 2015-07-15. A Comparison of Large Scale Dimension of a Metric Space to the Dimension of its Boundary. https://arxiv.org/abs/1507.04395

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