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From continua to $\mathbb{R}$–trees

Panos Papasoglu and Eric L Swenson

Algebraic & Geometric Topology 6 (2006) 1759–1784

arXiv: 0905.2576

Abstract

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