Volume 11, issue 5 (2011)

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The cactus tree of a metric space

Panos Papasoglu and Eric Swenson

Algebraic & Geometric Topology 11 (2011) 2547–2578
Abstract

We extend the cactus theorem of Dinitz, Karzanov, Lomonosov to metric spaces. In particular we show that if $X$ is a separable continuum which is not separated by $n-1$ points then the set of all $n$–tuples of points separating $X$ can be encoded by an $ℝ$–tree.

pretree, cuts
Mathematical Subject Classification 2000
Primary: 20E08, 54F15
Secondary: 20F65, 54F05, 05C40