Department of

September 2013 October 2013 November 2013 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 4 5 6 7 1 2 3 4 5 1 2 8 9 10 11 12 13 14 6 7 8 9 10 11 12 3 4 5 6 7 8 9 15 16 17 18 19 20 21 13 14 15 16 17 18 19 10 11 12 13 14 15 16 22 23 24 25 26 27 28 20 21 22 23 24 25 26 17 18 19 20 21 22 23 29 30 27 28 29 30 31 24 25 26 27 28 29 30

Thursday, October 31, 2013

**Abstract:** The study of outer automorphism group of a free group $Out(F_N)$ is closely related to study of Mapping Class Groups. The $Out(F_N)$ analog of a pseudo-Anosov homeomorphism is called a fully irreducible or iwip (short for irreducible with irreducible powers). We will talk about types of iwips, geometric and hyperbolic, and prove that any iwip $\phi$ acts on the space of geodesic currents with a certain kind of north-south dynamics. As an application, we will give a criterion for subgroups of $Out(F_N)$ to contain a hyperbolic iwip.