Domains of proper discontinuity on the boundary of Outer space

Details Domains of proper discontinuity on the boundary of Outer space Domains of proper discontinuity on the boundary of Outer space

2009-02-25

arxiv.org/abs/0902.4263v3

Illinois Journal of Mathematics, vol. 54 (2010), no. 1, pp. 89-108, special issue dedicated to Paul Schupp

Mathematics

Group Theory

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

Scientific paper

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.

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