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arXiv · 1807.04086

Finite cuts and CAT(0) boundaries

Panos Papasoglu·Eric Swenson
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Abstract

We show that if a 1-ended group $G$ acts geometrically on a CAT(0) space $X$ and $\bd X$ is separated by $m$ points then either $G$ is virtually a surface group or $G$ splits over a 2-ended group. In the course of the proof we study nesting actions on $\R $-trees and we show that nesting actions with non overlapping translation intervals give rise to isometric actions.

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Panos Papasoglu, Eric Swenson. 2018-07-11. Finite cuts and CAT(0) boundaries. https://arxiv.org/abs/1807.04086

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