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Thurston-Bennequin number of a Legendrian knot
Student-Run Geometry/Topology Seminar| Speaker: | Katia Fuchs, UC Davis |
| Location: | 593 Kerr |
| Start time: | Thu, Sep 1 2005, 1:10PM |
The general topic of my talk will be the Thurston Bennequin number, which is a bound assigned to Legendrian Knots. I will begin my talk by defining a Legendrian curve and subsequently a Legendrian knot. I will then discuss two possible projections of Legendrian knots (in one the pictures will have cusps, in the other they will not). Next I will introduce the Bennequin number, how to calculate it in the two projections, and look at several examples. I will show how the Bennquin number is a knot invariant, wherebey two knots which have different Bennequin numbers cannot be isomorphic. I will end with a few key results about the Thurston Bennequin number, and if time permits, a brief explanation of how the TB number is related to Knot Polynomials.