Accessibility, planar graphs, and quasi-isometries

Joseph Paul MacManus

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arXiv · 2310.15242

Accessibility, planar graphs, and quasi-isometries

Joseph Paul MacManus

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Abstract

We prove that a connected, locally finite, quasi-transitive graph which is quasi-isometric to a planar graph is necessarily accessible. This leads to a complete classification of the finitely generated groups which are quasi-isometric to planar graphs. In particular, such a group is virtually a free product of free and surface groups, and thus virtually admits a planar Cayley graph.

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Joseph Paul MacManus. 2023-10-23. Accessibility, planar graphs, and quasi-isometries. https://arxiv.org/abs/2310.15242

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