Return to Colloquia & Seminar listing
Invariants of Legendrian Knots
Student-Run Geometry/Topology Seminar| Speaker: | Dan Rutherford, UC Davis |
| Location: | 2112 MSB |
| Start time: | Thu, Jan 12 2006, 1:10PM |
The first invariants of Legendrian knots capable of distinguishing between knots of the same topological type were the rotation number and the Bennequin number. Until about the turn of the millenium no invariants were known to distinguish between Legendrian knots with equal Bennequin and rotation numbers and the same topological type. I will try to present two invariants which have this capability and use them to distinguish between two 5_2 knots with equal rotation and Bennequin numbers. The first is a complicated homological invariant and the second (not altogether unrelated) invariant is computed combinatorially from an xz-diagram for the knot. I will define everything above starting with the definition of a Legendrian knot.