Hyperbolic polyhedra and the Jones polynomial

Series: 
Geometry Topology Seminar
Monday, February 7, 2011 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
UCBerkeley
,  
For knots the hyperbolic geometry of the complement is known to be relatedto itsJones polynomial in various ways. We propose to study this relationship morecloselyby extending the Jones polynomial to graphs. For a planar graph we will showhow itsJones polynomial then gives rise to the hyperbolic volume of the polyhedronwhose1-skeleton is the graph. Joint with Francois Gueritaud and FrancoisCostantino.