Domains of proper discontinuity on the boundary of Outer space

Ilya Kapovich; Martin Lustig

Domains of proper discontinuity on the boundary of Outer space

Group Theory 2011-06-03 v3 Geometric Topology

Authors: Ilya Kapovich , Martin Lustig

Abstract

Motivated by the work of McCarthy and Papadopoulos for subgroups of mapping class groups, we construct domains of proper discontinuity in the compactified Outer space and in the projectivized space of geodesic currents for any "sufficiently large" subgroup of $Out(F_N)$ (that is, a subgroup containing a hyperbolic iwip). As a corollary we prove that for $N\ge 3$ the action of $Out(F_N)$ on the subset of $\mathbb PCurr(F_N)$ consisting of all projectivized currents with full support is properly discontinuous.

Keywords

Outer space proper discontinuity Out(F_N) geodesic currents hyperbolic iwip mapping class group

Cite

@article{arxiv.0902.4263,
  title  = {Domains of proper discontinuity on the boundary of Outer space},
  author = {Ilya Kapovich and Martin Lustig},
  journal= {arXiv preprint arXiv:0902.4263},
  year   = {2011}
}

Comments

Updated version, 16 pages; published in: Illinois J. Math. vol. 54 (2010), no. 1, pp. 89-108; special issue of IJM dedicated to Paul Schupp

Domains of proper discontinuity on the boundary of Outer space

Abstract

Keywords

Cite

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