Erratic Boundary Behavior of CAT(0) Geodesics under G-equivariant Maps

Dan Staley

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arXiv · 0911.2442

Erratic Boundary Behavior of CAT(0) Geodesics under G-equivariant Maps

Dan Staley

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Abstract

We show that, given any finite dimensional, connected, compact metric space Z, there exists a group G acting geometrically on two CAT(0) spaces X and Y, a G-equivariant quasi-isometry f from X to Y, and a geodesic ray c in X, such that the closure of f(c), instersected with the boundary of Y, is homeomorphic to Z. This characterizes all homeomorphism types of "geodesic boundary images" that arise in this manner.

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Dan Staley. 2009-11-12. Erratic Boundary Behavior of CAT(0) Geodesics under G-equivariant Maps. https://arxiv.org/abs/0911.2442

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