TY - JOUR
T1 - Domains of proper discontinuity on the boundary of outer space
AU - Kapovich, Ilya
AU - Lustig, Martin
PY - 2010
Y1 - 2010
N2 - 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 "dynamically large" subgroup of Out(FN) (that is, a subgroup containing an atoroidal iwip). As a corollary, we prove that for N≥3 the action of Out(FN) on the subset of ℙCurr(FN) consisting of all projectivized currents with full support is properly discontinuous.
AB - 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 "dynamically large" subgroup of Out(FN) (that is, a subgroup containing an atoroidal iwip). As a corollary, we prove that for N≥3 the action of Out(FN) on the subset of ℙCurr(FN) consisting of all projectivized currents with full support is properly discontinuous.
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U2 - 10.1215/ijm/1299679739
DO - 10.1215/ijm/1299679739
M3 - Article
AN - SCOPUS:80052716975
SN - 0019-2082
VL - 54
SP - 89
EP - 108
JO - Illinois Journal of Mathematics
JF - Illinois Journal of Mathematics
IS - 1
ER -