Lines of minima in Outer space

Details Lines of minima in Outer space Lines of minima in Outer space

2009-11-18

arxiv.org/abs/0911.3620v2

Mathematics

Geometric Topology

Writing improved. Minor corrections. References corrected. 26 p

Scientific paper

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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