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arXiv · 1909.12360

Boundaries of groups with isolated flats are path connected

Michael Ben-Zvi
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Abstract

A seminal result in geometric group theory is that a 1-ended hyperbolic group has a locally connected visual boundary. As a consequence, a 1-ended hyperbolic group also has a path connected visual boundary. In this paper, we study when this phenomenon occurs for CAT(0) groups. We show if a 1-ended CAT(0) group with isolated flats acts geometrically on a CAT(0) space, then the visual boundary of the space is path connected. As a corollary, we prove all CAT(0) groups with isolated flats are semistable at infinity.

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Michael Ben-Zvi. 2019-09-26. Boundaries of groups with isolated flats are path connected. https://arxiv.org/abs/1909.12360

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