Acylindrical accessibility for groups

@article{Sela1997AcylindricalAF,
  title={Acylindrical accessibility for groups},
  author={Zlil Sela},
  journal={Inventiones mathematicae},
  year={1997},
  volume={129},
  pages={527-565}
}
  • 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… 
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