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Spring 2010 Domains of proper discontinuity on the boundary of Outer space
Ilya Kapovich, Martin Lustig
Illinois J. Math. 54(1): 89-108 (Spring 2010). DOI: 10.1215/ijm/1299679739

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 “dynamically large” subgroup of $\operatorname{Out}(F_N)$ (that is, a subgroup containing an atoroidal iwip).

As a corollary, we prove that for $N\ge3$ the action of $\operatorname{Out}(F_N)$ on the subset of $\mathbb{P}\operatorname{Curr}(F_N)$ consisting of all projectivized currents with full support is properly discontinuous.

Citation

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Ilya Kapovich. Martin Lustig. "Domains of proper discontinuity on the boundary of Outer space." Illinois J. Math. 54 (1) 89 - 108, Spring 2010. https://doi.org/10.1215/ijm/1299679739

Information

Published: Spring 2010
First available in Project Euclid: 9 March 2011

zbMATH: 1259.20050
MathSciNet: MR2776986
Digital Object Identifier: 10.1215/ijm/1299679739

Subjects:
Primary: 20F
Secondary: 37B, 37D, 57M

Rights: Copyright © 2010 University of Illinois at Urbana-Champaign

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Vol.54 • No. 1 • Spring 2010
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