## Domains of proper discontinuity on the boundary of outer space.(English)Zbl 1259.20050

The authors construct domains of discontinuity in the compactified Outer space and in the projectivized space of geodesic currents for any “dynamically large” subgroup of $$\mathrm{Out}(F_N)$$. The work is motivated by the work of J. McCarthy and A. Papadopoulos [Comment. Math. Helv. 64, No. 1, 133-166 (1989; Zbl 0681.57002)]. As a corollary, the authors prove that for any $$N>3$$, the action of $$\mathrm{Out}(F_N)$$ on the subset of the projectivized space of geodesic currents consisting of all projectivized currents with full support is properly discontinuous.

### MSC:

 20F65 Geometric group theory 20E36 Automorphisms of infinite groups 37C85 Dynamics induced by group actions other than $$\mathbb{Z}$$ and $$\mathbb{R}$$, and $$\mathbb{C}$$ 57M07 Topological methods in group theory

Zbl 0681.57002
Full Text:

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