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

- Date: 11/30/2006

Lecturer(s):

Melissa Macasieb (University of British Columbia)

Location:

University of British Columbia

Topic:

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