Contracting orbits in Outer space

@article{Dowdall2019ContractingOI,
  title={Contracting orbits in Outer space},
  author={Spencer Dowdall and Samuel J. Taylor},
  journal={Mathematische Zeitschrift},
  year={2019},
  volume={293},
  pages={767-787}
}
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 $${{\,\mathrm{Out}\,}}(\mathbb {F})$$Out(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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References

SHOWING 1-10 OF 32 REFERENCES

Stability in Outer Space

We characterize strongly Morse quasi-geodesics in Outer space as quasi-geodesics which project to quasi-geodesics in the free factor graph. We define convex cocompact subgroups of $Out(F_n)$ as

Strongly Contracting Geodesics in Outer Space

We study the Lipschitz metric on Outer Space and prove that fully irreducible elements of Out(F_n) act by hyperbolic isometries with axes which are strongly contracting. As a corollary, we prove that

Lines of minima in outer space

We define lines of minima in the thick part of Outer space for the free group Fn with n>2 generators. We show that these lines of minima are contracting for the Lipschitz metric. Every fully

Asymmetry of Outer space

We study the asymmetry of the Lipschitz metric d on Outer space. We introduce an (asymmetric) Finsler norm $${\|\cdot\|^L}$$ that induces d. There is an Out(Fn)-invariant “potential” Ψ defined on

Quasi-projections in Teichmüller space.

where d(x, C) = inf d(x, C). (Provided Xis proper, i.e. /?-balls are compact, nc(x) is never yeC empty.) Suppose now that X is a simply-connected Riemannian manifold with non-positive sectional

Cannon–Thurston maps for hyperbolic free group extensions

This paper gives a detailed analysis of the Cannon–Thurston maps associated to a general class of hyperbolic free group extensions. Let F denote a free group of finite rank at least 3 and consider a

The Gromov topology on R-trees

The boundary of the free splitting graph and the free factor graph

We show that the Gromov boundary of the free factor graph for the free group Fn with n>2 generators is the space of equivalence classes of minimal very small indecomposable projective Fn-trees

THE BOUNDARY OF THE FREE FACTOR GRAPH AND THE FREE SPLITTING GRAPH

We show that the Gromov boundary of the free factor graph for the free group Fn with n ≥ 3 generators is the space of equivalence classes of minimal very small indecomposable projective Fn-trees

The expansion factors of an outer automorphism and its inverse

A fully irreducible outer automorphism o of the free group F n of rank n has an expansion factor which often differs from the expansion factor of o -1 Nevertheless, we prove that the ratio between