Geometry and Topology Seminar
Deformation spaces of
G
-trees
Matt Clay, University of Oklahoma
Details
Wednesday October 11, 2006
809 Physical Sciences Center
3:45 pm
Abstract
Deformation spaces of
G
-trees are a generalization of Culler and Vogtmann's outer space for a finitely generated group
G
. These spaces were introduced by Forester. We will show that like outer space, deformation spaces are contractible. This was independently proved by Guirardel and Levitt. We will present an equivariant deformation retract and discuss some instances when it is finite dimensional. This deformation retract can be explicitly construsted for the classical Baumslag-Solitar groups
BS(p,q)
. Using the action of
Out(BS(p,q))
on the deformation space, we can give a presentation for
Out(BS(p,q))
in the interesting case where
p
properly divides
q
. This reproves an algebraic calculation of Collins and Levin.