LINES OF MINIMA IN OUTER SPACE

We define lines of minima in the thick part of outer space for the free group F-n with n >= 3 generators. We show that these lines of minima are contracting for the Lipschitz metric. Every fully irreducible outer automorphism of F-n defines such a line of minima. Now let Gamma be a subgroup of the outer automorphism group of F-n which is not virtually abelian. We obtain that if Gamma contains at least one fully irreducible element, then for every p is an element of (1, infinity) the second bounded cohomology group H-b(2)(Gamma, l(p) (Gamma)) is infinite-dimensional.