Lines of minima in Outer space

Abstract

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 irreducible outer automorphism of Fn defines such a line a minima. Now let G be a subgroup of the outer automorphism group of Fn which is not virtually abelian. We obtain as an immediate application that if G contains at least one fully irreducible element then for every p<1 the second bounded cohomology group with coefficients in lp(G) is infinite dimensional.

arXiv commentFinal version. 35 p

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Cited by in corpus (13)

• Induced quasi-cocycles on groups with hyperbolically embedded subgroups
• The boundary of the free splitting graph and the free factor graph
• The isometry group of Outer Space
• The Poisson boundary of $\text{Out}(F_N)$
• Dynamics of hyperbolic iwips
• Subset currents on free groups
• Ideal Whitehead Graphs in Out(F_r) II: The Complete Graph in Each Rank
• Hyperbolic actions and 2nd bounded cohomology of subgroups of $\text{Out}(F_n)$. Part I: Infinite lamination subgroups
• Twisting out fully irreducible automorphisms
• Patterson-Sullivan currents, generic stretching factors and the asymmetric Lipschitz metric for Outer space
• Relative twisting in Outer space
• Random length-spectrum rigidity for free groups
• Generic-case complexity of Whitehead's algorithm, revisited