On the Legendrian and transverse classification of cabled knot types

Geometry Topology Seminar
Monday, November 9, 2009 - 2:00pm
1 hour (actually 50 minutes)
Skiles 269
Ga Tech
In 3-dimensional  contact topology one of the main problem  is classifying Legendrian (transverse) knots in certain knot type up to Legendrian ( transverse) isotopy. In particular we want to decide if two (one in case of transverse knots) classical invariants of this knots are complete set of invariants. If it is, then we call this knot type Legendrian (transversely) simple knot type otherwise it is called Legendrian (transversely)  non-simple. In this talk, by tracing the techniques developed by Etnyre and Honda, we will present some  results  concerning  the complete Legendrian and transverse classification of certain cabled knots in the  standard tight contact 3-sphere. Moreover we will provide an infinite family of  Legendrian  and  transversely non-simple prime knots.