PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Augustin Banyaga.

Title:KNOTS IN CONTACT GEOMETRY
Seminar:Symplectic Topology Seminar
Speaker:Dmitry Fuchs, UC (Davis)
Abstract:
I will consider Legendrian knots in the standard contact space. There are classical (the Thurston-Bennequin and rotation numbers) and more modern (contact homology) Legendrian isotopy invariants of Legendrian knots. A (generic) Legendrian knot is determined by its xz-projection (aka the front projection) which is a smooth closed curve in the plane with transverse self-intersections and cusps but without vertical tangents and self-tangencies. In the early 2000's, a visualizable combinatorial structure on front diagram was discovered (independently, by Chekanov, Pushkar, and the speaker); it is called a normal ruling. The existence of a normal ruling turns out to be necessary and sufficient for some seemingly unrelated properties of Legendrian knots, such as the existence of a generating family of functions, existence of augmentations in the Chekanov-Eliashberg DGA and exactness of known estimates of the Thurston-Bennequin number in topological terms (knot polynomials). The talk will contain a survey of results of this kind with an emphasis on a recently discovered connections between the generating families and the contact homology.

Room Reservation Information

Room Number:MB216
Date:03 / 06 / 2008
Time:02:15pm - 03:45pm