Mathematics – Group Theory
Scientific paper
2009-02-25
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.
Kapovich Ilya
Lustig Martin
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