Geometry, Topology and Dynamics Seminar
Catherine Pfaff
Universite d'Aix Marseille
Lone Axes in Outer Space
Abstract: (Joint work with Lee Mosher)
As with $\mathrm{SL}(2,R)$ acting on hyperbolic space, a central method for studying a mapping class group is to study its action
on its Teichmuller space and a central method for studying an outer automorphism group of a free group $\mathrm{Out}(F_n)$ is to
study its action on its Culler-Vogtmann outer space $\mathrm{CV}_n$. Each of these groups also have elements acting in some sense
hyperbolically (pseudo-Anosov elements of mapping class groups and fully irreducible outer automorphisms of free groups).
However, the analogy breaks down when one wants to study the invariant axis for a fully irreducible. It appears the
correct object to study is actually a collection of axes, an "axis bundle." By proving when the axis bundle for a fully
irreducible is just a single axis, we have highlighted the setting where a fully irreducible also behaves in this regard
like a pseudo-Anosov or hyperbolic element. In fact, we have identified a setting where one can actually quite easily
identify when two fully irreducibles are conjugate.
Monday November 4, 2013 at 3:00 PM in SEO 636