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arXiv · 1910.01797

The space of directions for hyperbolic totally disconnected locally compact groups

Timothy P. Bywaters
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Abstract

The space of directions is a notion of boundary associated to an arbitrary totally disconnected locally compact group. We explicitly calculate the space of directions of a group acting vertex transitively with compact open vertex stabilisers on a locally finite connected hyperbolic graph. These are examples of groups where techniques from geometric group theory can be generalised from the discrete to the non-discrete case. We show the space of directions for these groups is a discrete metric space. Our results resolve a conjecture of Baumgartner, M\"oller and Willis in the affirmative.

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Timothy P. Bywaters. 2019-10-04. The space of directions for hyperbolic totally disconnected locally compact groups. https://arxiv.org/abs/1910.01797

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