Logic Seminar
Patrick Reynolds
University of Utah
An asymptotic invariant for free group outer automorphisms from the non-standard point of view
Abstract: For F a free group and $\Phi \in$ Out(F) an element of infinite
order, a fruitful approach for studying the structure of $\Phi$ is to
construct from $\Phi$ an isometric action of F on an $\mathbb{R}$-tree
$T_{\Phi}$ that is preserved by $\Phi$ in an appropriate sense. The idea is
that certain aspects of the structure of $\Phi$ are reflected in the
structure of $T_{\Phi}$. The typical procedure for constructing $T_{\Phi}$ is
to use the equivariant Gromov topology on the space of F-spaces. The
point of this talk is to give a simple construction of $T_{\Phi}$ from the
point of view of non-standard analysis. We will further explain that the
non-standard picture makes clear how to construct a more sensitive
invariant, and we will give a discussion of the advantages of this new
invariant. Relevant group theory and non-standard analysis background
will be given, so the talk should be generally accessible.
Tuesday October 9, 2012 at 2:00 PM in SEO 427