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arxiv: 1502.04053 · v3 · pith:PHVZRRDZnew · submitted 2015-02-13 · 🧮 math.GT · math.GR

Contracting orbits in Outer space

classification 🧮 math.GT math.GR
keywords contractingouterspacecomplexfactorfreegeodesicsstrongly
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We show that strongly contracting geodesics in Outer space project to parameterized quasigeodesics in the free factor complex. This result provides a converse to a theorem of Bestvina--Feighn, and is used to give conditions for when a subgroup of $\mathrm{Out}(\mathbb{F})$ has a quasi-isometric orbit map into the free factor complex. It also allows one to construct many new examples of strongly contracting geodesics in Outer space.

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