Trees of cylinders and canonical splittings

Details Trees of cylinders and canonical splittings Trees of cylinders and canonical splittings

2008-11-14

arxiv.org/abs/0811.2383v2

Mathematics

Group Theory

38 pages, 2 figures. Reference update

Scientific paper

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, co-elementarity 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).

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