Geometry & Topology
- Geom. Topol.
- Volume 15, Number 2 (2011), 977-1012.
Trees of cylinders and canonical splittings
Let be a tree with an action of a finitely generated group . Given a suitable equivalence relation on the set of edge stabilizers of (such as commensurability, coelementarity in a relatively hyperbolic group, or commutation in a commutative transitive group), we define a tree of cylinders . This tree only depends on the deformation space of ; in particular, it is invariant under automorphisms of if is a JSJ splitting. We thus obtain –invariant cyclic or abelian JSJ splittings. Furthermore, has very strong compatibility properties (two trees are compatible if they have a common refinement).
Geom. Topol., Volume 15, Number 2 (2011), 977-1012.
Received: 10 December 2008
Accepted: 29 March 2011
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20E08: Groups acting on trees [See also 20F65]
Secondary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20F67: Hyperbolic groups and nonpositively curved groups 20E06: Free products, free products with amalgamation, Higman-Neumann- Neumann extensions, and generalizations
Guirardel, Vincent; Levitt, Gilbert. Trees of cylinders and canonical splittings. Geom. Topol. 15 (2011), no. 2, 977--1012. doi:10.2140/gt.2011.15.977. https://projecteuclid.org/euclid.gt/1513732309