The hyperbolic volume and Jones polynomial of an embedded graph

Series: 
Geometry Topology Seminar
Monday, September 8, 2008 - 14:00
1 hour (actually 50 minutes)
Location: 
Skiles 269
,  
University of Amsterdam
The hyperbolic volume and the colored Jones polynomial are two of the most powerful invariants in knot theory. In this talk we aim to extend these invariants to arbitrary graphs embedded in 3-space. This provides new tools for studying questions about graph embedding and it also sheds some new light on the volume conjecture. According to this conjecture, the Jones polynomial and the volume of a knot are intimately related. In some special cases we will prove that this still holds true in the case of graphs.