Lines of minima in Outer space

Ursula Hamenstaedt

doi:10.1215/00127094-2429807

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arXiv · 0911.3620

Lines of minima in Outer space

Ursula Hamenstaedt

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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.

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Ursula Hamenstaedt. 2013-09-19. Lines of minima in Outer space. https://doi.org/10.1215/00127094-2429807

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