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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 –tree.

Keywords
pretree, cuts
Mathematical Subject Classification 2000
Primary: 20E08, 54F15
Secondary: 20F65, 54F05, 05C40
References
Publication
Received: 1 September 2010
Revised: 23 January 2011
Accepted: 14 April 2011
Published: 13 September 2011
Authors
Panos Papasoglu
Mathematical Institute
University of Oxford
24-29 St Giles’
Oxford OX1 3LB
UK
http://users.uoa.gr/~ppapazog/
Eric Swenson
Mathematics Department
Brigham Young University
Provo UT 84602
USA