Trees of cylinders and canonical splittings
By Vincent Guirardel, Gilbert Levitt. 2008
58 citations recorded by the source corpus.
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).
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d67776e00e424639b338fb2aae8f4301bbbef17f
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In Discrete Mathematics and Combinatorics
- Franccois Dahmani
- Vincent Guirardel
- Alessandro Sisto
- Denis V. Osin
- Jason A. Behrstock
- Gilbert Levitt
In Geometry and Topology
- Vincent Guirardel
- Franccois Dahmani
- Denis V. Osin
- Alessandro Sisto
- Gilbert Levitt
- D. Groves
- Henry Wilton
- Nathanial P. Brown Narutaka Ozawa
In Mathematical Physics
- Vincent Guirardel
- Franccois Dahmani
- Denis V. Osin
- Alessandro Sisto
- Gilbert Levitt
- D. Groves
- Henry Wilton
- Nathanial P. Brown Narutaka Ozawa
Citations in the corpus
- The Isomorphism Problem for All Hyperbolic Groups (2010, background): “The tree Tc is the bipartite G-tree whose vertex set is V (Tc) = V0(Tc)⊔V1(Tc), and where x ∈ V0(Tc) and Y ∈ V1(Tc) are connected by an edge (x, Y ) if and only if x ∈ Y (see [GL08] for details).”