The cactus tree of a metric space

Papasoglu, Panos; Swenson, Eric

doi:10.2140/agt.2011.11.2547

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The cactus tree of a metric space

Panos Papasoglu and Eric Swenson

Algebraic & Geometric Topology 11 (2011) 2547–2578

DOI: 10.2140/agt.2011.11.2547

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.

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

Volume 11, issue 5 (2011)