Geometry & Topology 15 (2011) 977–1012

DOI: 10.2140/gt.2011.15.977

Abstract

Let T be a tree with an action of a finitely generated group G. Given a suitable equivalence relation on the set of edge stabilizers of T (such as commensurability, coelementarity in a relatively hyperbolic group, or commutation in a commutative transitive group), we define a tree of cylinders T_c. This tree only depends on the deformation space of T; in particular, it is invariant under automorphisms of G if T is a JSJ splitting. We thus obtain Out(G)–invariant cyclic or abelian JSJ splittings. Furthermore, T_c has very strong compatibility properties (two trees are compatible if they have a common refinement).

Keywords

JSJ decomposition, canonical decomposition, amalgamated free product

Mathematical Subject Classification

Primary: 20E08

Secondary: 20E06, 20F65, 20F67

References

Publication

Received: 10 December 2008
Accepted: 29 March 2011
Published: 22 June 2011
Proposed: Martin Bridson
Seconded: Benson Farb, Danny Calegari

Authors