Legendrian and transverse knots

September 15 to September 19, 2008

at the

American Institute of Mathematics, Palo Alto, California

organized by

Dmitry Fuchs, Serge Tabachnikov, and Lisa Traynor

Original Announcement

This workshop concerns Legendrian and transverse knots in contact three-dimensional manifolds. The focus will be on the interplay between topological knot theory and contact topology. The study of knots in contact space goes back to the early 1980s when D. Bennequin used knots to establish the existence of exotic contact structures. Since the late 1990s this area has experienced a surge of activity, after the work of Yu. Chekanov and Ya. Eliashberg on the contact homology of Legendrian knots.

One of the main goals of the workshop is to achieve a better understanding of a somewhat mysterious combinatorial structure of front diagrams of Legendrian knots, the so-called, normal rulings. This structure is closely related to seemingly independent properties of Legendrian knots: the existence of generating families of functions, certain algebraic properties of the Chekanov--Eliashberg algebra (augmentations), and the sharpness of the estimates of the self-linking (Thurston--Bennequin) numbers of Legendrian knots. A second goal is to make progress in the study of transverse knots, in particular, by constructing transverse invariants of the contact homology type. Further goals include applying Legendrian knot theory to topological knot theory and finding applications of Legendrian knot theory to global singularity theory in the spirit of Chekanov and Pushkar�s recent proof of Arnold's four cusps conjecture.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.