Alexandra Pettet

The outer automorphism group Out(F) of a free group F of finite rank shares many properties with the mapping class group of a surface, however the techniques for studying these groups are generally quite different. Analogues of the pseudo-Anosov...

Abstract: Fully irreducible outer automorphisms of a free group are analogous to loxodromic isometries of hyperbolic space, or to pseudo-Anosov elements of the mapping class group of a surface. We develop methods for constructing customized fully...

The notion of relative twisting of curves on a surface, the special case of subsurface projection to an annulus, is an important tool in the theory of mapping class groups. We develop an analogue for the outer automorphisms of a free group. This is...