The no-short-separating-arc conjecture for CAT(0) boundaries

Let GG be a one-ended group acting geometrically on a CAT(0) space XX, and let X\partial X denote its boundary. Assume that X\partial X has no finite cut. No-short-separating-arc conjecture. No arc of Tits length <2π<2\pi separates X\partial X. This conjecture proposes that, in the absence of finite cuts, CAT(0) boundaries cannot be separated by sufficiently short Tits-geodesic arcs; its status is not resolved in the supplied source.

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Primary source

Panos Papasoglu and Eric Swenson, “Finite cuts and CAT(0) boundaries”, arXiv:1807.04086 (2018).

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