# Finite cuts and CAT(0) boundaries

Papasoglu, P
Swenson, E

## Last Updated:

2020-05-06T15:45:19.193+01:00

## 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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