Abstract
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).
Citation
Vincent Guirardel. Gilbert Levitt. "Trees of cylinders and canonical splittings." Geom. Topol. 15 (2) 977 - 1012, 2011. https://doi.org/10.2140/gt.2011.15.977
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