Contracting orbits in Outer space

Spencer Dowdall; Samuel J. Taylor

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arXiv · 1502.04053

Contracting orbits in Outer space

Spencer Dowdall·Samuel J. Taylor

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Abstract

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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Spencer Dowdall, Samuel J. Taylor. 2015-02-13. Contracting orbits in Outer space. https://arxiv.org/abs/1502.04053

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