On the Legendrian and transverse classification of cabled knot types

Series
Geometry Topology Seminar
Time
Monday, November 9, 2009 - 2:00pm for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Bulent Tosun – Ga Tech
Organizer
John Etnyre
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.