A generalisation of the deformation variety

Geometry Topology Seminar
Monday, October 12, 2009 - 2:05pm for 2 hours
Skiles 269
Henry Segerman – UTexas Austin – henrys@math.utexas.eduhttp://www.ma.utexas.edu/users/henrys/
Stavros Garoufalidis
The deformation variety is similar to the representation variety inthat it describes (generally incomplete) hyperbolic structures on3-manifolds with torus boundary components. However, the deformationvariety depends crucially on a triangulation of the manifold: theremay be entire components of the representation variety which can beobtained from the deformation variety with one triangulation but notanother, and it is unclear how to choose a "good" triangulation thatavoids these problems. I will describe the "extended deformationvariety", which deals with many situations that the deformationvariety cannot. In particular, given a manifold which admits someideal triangulation we can construct a triangulation such that we canrecover any irreducible representation (with some trivial exceptions)from the associated extended deformation variety.