Departmental Colloquium
Sergei Chmutov
Ohio State University, Mansfield
Legendrian and transversal knots and their invariants
Abstract: Legendrian knots are knots in a 3-manifold with an additional structure, contact structure. This is a non-integrable field of tangent 2-planes. A Legendrian knot tangents the 2-planes at each point. A transversal knot is transverse to the 2-planes at each point. The presence of the contact structure refines the topological equivalence of knots. For each topological type of knots there are a Legendrian and a transversal representatives. There are simple invariants of Legendian and traversal equivalences withing the same topological type. More delicate invariants come from modern homology theories, contact homology, Khovanov homology and Floer homology. The talk with be a survey of the area of Legendrian and transversal knots. I will explain the front diagrams of Legendrian knots, the braid diagrams of transversal knots, formulate the versions of the Reidemeister moves for these knots, define the simplest invariants, and survey the modern homological invariants.
This lecture is part of Knots in Chicago (September 10-12, 2010).
Friday September 10, 2010 at 3:00 PM in SEO 636