From continua to ℝ–trees

Papasoglu, Panos; Swenson, Eric L

doi:10.2140/agt.2006.6.1759

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From continua to $\mathbb{R}$–trees

Panos Papasoglu and Eric L Swenson

Algebraic & Geometric Topology 6 (2006) 1759–1784

DOI: 10.2140/agt.2006.6.1759

arXiv: 0905.2576

Abstract

We show how to associate an $ℝ$ –tree to the set of cut points of a continuum. If $X$ is a continuum without cut points we show how to associate an $ℝ$ –tree to the set of cut pairs of $X$ .

Keywords

continuum, cut point, JSJ decomposition

Mathematical Subject Classification 2000

Primary: 54F15, 20E08

Secondary: 54F05, 20F65

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Publication

Received: 31 May 2006

Revised: 25 August 2006

Accepted: 26 August 2006

Published: 1 November 2006

Authors

Panos Papasoglu
Mathematics Department University of Athens Athens 157 84 Greece

Eric L Swenson
Mathematics Department Brigham Young University Provo UT 84602 USA

Volume 6, issue 4 (2006)