The action on a tree associated to an ideal point of the character variety

  • Date: 11/30/2006

Melissa Macasieb (University of British Columbia)


University of British Columbia


Let G be the fundamental group of a compact, orientable, irreducible
3-manifold M. I will discuss the correspondence between ideal points of
a curve in the character variety X(G) and actions of G on a tree
(following Culler-Shalen). This is a particular case of Bass-Serre
theory concerning subgroups of SL_2(K), where K is a local field. I
will spend some time discussing the tree for SL_2(K) and its relation
to graphs of groups, and time permitting, how this relates to the
existence of incompressible surfaces in M.

Other Information: 

Algebraic Topology Seminar 2006