Algebraic & Geometric Topology

From continua to $\mathbb{R}$–trees

Panos Papasoglu and Eric L Swenson

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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.

Article information

Algebr. Geom. Topol., Volume 6, Number 4 (2006), 1759-1784.

Received: 31 May 2006
Revised: 25 August 2006
Accepted: 26 August 2006
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 54F15: Continua and generalizations 20E08: Groups acting on trees [See also 20F65]
Secondary: 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces [See also 06B30, 06F30] 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]

continuum cut point JSJ decomposition


Papasoglu, Panos; Swenson, Eric L. From continua to $\mathbb{R}$–trees. Algebr. Geom. Topol. 6 (2006), no. 4, 1759--1784. doi:10.2140/agt.2006.6.1759.

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