For more information about this meeting, contact Augustin Banyaga.
| Title: | KNOTS IN CONTACT GEOMETRY |
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| Seminar: | Symplectic Topology Seminar |
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| Speaker: | Dmitry Fuchs, UC (Davis) |
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| Abstract: |
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| 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 |
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| Date: | 03 / 06 / 2008 |
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| Time: | 02:15pm - 03:45pm |
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