Acylindrical accessibility for groups

  title={Acylindrical accessibility for groups},
  author={Zlil Sela},
  journal={Inventiones mathematicae},
  • Z. Sela
  • Published 1 August 1997
  • Mathematics
  • Inventiones mathematicae
Abstract.We define the notion of acylindrical graph of groups of a group. We bound the combinatorics of these graphs of groups for f.g. freely indecomposable groups. Our arguments imply the finiteness of acylindrical surfaces in closed 3-manifolds [Ha], finiteness of isomorphism classes of small splittings of (torsion-free) freely indecomposable hyperbolic groups as well as finiteness results for small splittings of f.g. Kleinian and semisimple discrete groups acting on non-positively curved… 
Acylindrical actions on CAT(0) square complexes
For group actions on hyperbolic CAT(0) square complexes, we show that the acylindricity of the action is equivalent to a weaker form of acylindricity phrased purely in terms of stabilisers of points,
Acylindrically hyperbolic groups and their quasi-isometrically embedded subgroups
We abstract the notion of an A/QI triple from a number of examples in geometric group theory. Such a triple (G,X,H) consists of a group G acting on a Gromov hyperbolic space X, acylindrically along a
Limit groups for relatively hyperbolic groups. I. The basic tools
We begin the investigation of -limit groups, where is a torsion-free group which is hyperbolic relative to a collection of free abelian subgroups. Using the results of (16), we adapt the re- sults
Non-positively curved complexes of groups and boundaries
Given a complex of groups over a finite simplicial complex in the sense of Haefliger, we give conditions under which it is possible to build an EZ ‐structure in the sense of Farrell and Lafont for
Largest acylindrical actions and Stability in hierarchically hyperbolic groups
We consider two manifestations of non-positive curvature: acylindrical actions (on hyperbolic spaces) and quasigeodesic stability. We study these properties for the class of hierarchically hyperbolic
Limit groups and Makanin-Razborov diagrams for hyperbolic groups
This thesis gives a detailed description of Zlil Sela’s construction of Makanin-Razborov diagrams which describe Hom(G,Γ), the set of all homomorphisms from G to Γ, where G is a finitely generated
Structure and Rigidity in (Gromov) Hyperbolic Groups and Discrete Groups in Rank 1 Lie Groups II
Abstract. We borrow the Jaco-Shalen-Johannson notion of characteristic sub-manifold from 3-dimensional topology to study cyclic splittings of torsion-free (Gromov) hyperbolic groups and finitely
Invariant subalgebras of von Neumann algebras arising from negatively curved groups
Using an interplay between geometric methods in group theory and soft von Neuman algebraic techniques we prove that for any icc, acylindrically hyperbolic group Γ its von Neumann algebra L (Γ)
McCool groups of toral relatively hyperbolic groups
The outer automorphism group Out(G) of a group G acts on the set of conjugacy classes of elements of G. McCool proved that the stabilizer $Mc(c_1,...,c_n)$ of a finite set of conjugacy classes is