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Trees of cylinders and
canonical splittings
Vincent Guirardel and Gilbert Levitt |
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Geometry & Topology 15 (2011) 977–1012
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Abstract |
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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). |
Keywords
JSJ decomposition, canonical decomposition, amalgamated
free product
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Mathematical Subject Classification 2000
Primary: 20E08
Secondary: 20F65, 20F67, 20E06
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References |
Publication
Received: 10 December 2008
Accepted: 29 March 2011
Published: 22 June 2011
Proposed: Martin Bridson
Seconded: Benson Farb, Danny Calegari
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Authors |
| Vincent Guirardel | |
| Institut de Mathématiques de
Toulouse Université de Toulouse CNRS (UMR 5219) 118 route de Narbonne F-31062 Toulouse cedex 9 France |
Institut de Recherche Mathématiques
de Rennes Université de Rennes 1 CNRS (UMR 6625) 263 avenue du General Leclerc CS 74205 35042 Rennes Cedex France |
| http://perso.univ-rennes1.fr/vincent.guirardel/ | |
| Gilbert Levitt | |
| Laboratoire de Mathématiques Nicolas
Oresme Université de Caen CNRS (UMR 6139) BP 5186 F-14032 Caen Cedex France |
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