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Cutpoints of CAT(0) groups

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NPCW01 - Non-positive curvature in action

(Joint with Eric Swenson)
It is known that if the boundary of a 1-ended hyperbolic group G has a local cut point then G splits over a 2-ended group. We prove a similar theorem for CAT groups, namely that if a finite set of points separates the boundary of a 1-ended CAT group G
then G splits over a 2-ended group. Along the way we prove two results of independent interest: we show that continua separated
by finite sets of points admit a tree-like decomposition and we show a splitting theorem for nesting actions on R-trees.

This talk is part of the Isaac Newton Institute Seminar Series series.

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