We define lines of minima in the thick part of outer space for the free group with generators. We show that these lines of minima are contracting for the Lipschitz metric. Every fully irreducible outer automorphism of defines such a line of minima. Now let be a subgroup of the outer automorphism group of which is not virtually abelian. We obtain that if contains at least one fully irreducible element, then for every the second bounded cohomology group is infinite-dimensional.
"Lines of minima in outer space." Duke Math. J. 163 (4) 733 - 776, 15 March 2014. https://doi.org/10.1215/00127094-2429807