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arXiv · 2511.15855

Paths in graphs: bounded geometry and property A

V. Manuilov
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Abstract

We expose a class of discrete metric spaces, for which bounded geometry is equivalent to the property A of G. Yu. This class includes the coarse disjoint union of $(\mathbb Z/2\mathbb Z)^n$, $n\in\mathbb N$, and consists of spaces of simple paths in a class of graphs that includes cactus graphs, with the metric defined as the number of edges in the symmetric difference of the paths. We also show that if a space in this class does not have bounded geometry then it contains a subspace of bounded geometry without property A.

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V. Manuilov. 2025-11-19. Paths in graphs: bounded geometry and property A. https://arxiv.org/abs/2511.15855

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