Boundaries of groups with isolated flats are path connected
17 Oct 2019
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Ben-Zvi Michael
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.(read more)