The uniform thickness property and iterated torus knots

Geometry Topology Seminar
Monday, September 21, 2009 - 14:00
1 hour (actually 50 minutes)
Skiles 269
SUNY - Buffalo
The uniform thickness property (UTP) is a property of knots embeddedin the 3-sphere with the standard contact structure. The UTP was introduced byEtnyre and Honda, and has been useful in studying the Legendrian and transversalclassification of cabled knot types.  We show that every iterated torus knotwhich contains at least one negative iteration in its cabling sequence satisfiesthe UTP.  We also conjecture a complete UTP classification for iterated torusknots, and fibered knots in general.