Amalgam Anosov representations
Matt Stover (Temple)
Abstract:
Let \Gamma be a torsion-free hyperbolic group and G a semisimple Lie
group. Then Out(\Gamma) acts on the character variety of
representations from \Gamma into G. When \Gamma is a closed surface
group and G is PSL_2(R), the action is properly discontinuous on the
two components coming from Teichmuller space, and Goldman conjectured
that this is the maximal such open domain. A candidate analogue in the
general case are the so-called Anosov representations, which exhibit
many of the important geometric and dynamical properties of
representations in Teichmuller space. I will explain how one can use
the JSJ decomposition of the hyperbolic group to build domains that
are often strictly larger than the Anosov representations on which the
Out(\Gamma)-action remains properly discontinuous: the amalgam Anosov
representations. The talk will contain lots of examples from
low-dimensional topology.
This is joint work with Richard Canary, Michelle Lee (and Andres
Sambarino, if I have time).