Loose Legendrian Knots in High Dimensional Contact Manifolds

Geometry Topology Seminar
Monday, December 5, 2011 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 005
Emmy Murphy – Stanford University
John Etnyre
In the talk, I plan to give a definition of loose Legendrian knots inside contact manifolds of dimension 5 or greater. The definition is significantly different from the 3 dimensional case, in particular loose knots exist in local charts. I'll discuss an h-principle for such knots. This implies their classification, a bijective correspondence with their formal (algebraic topology) invariants. I'll also discuss applications of this result, comparisons with 3D contact toplogy, and some open questions.