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Invariants of Legendrian Knots
Student-Run Geometry/Topology| Speaker: | Dan Rutherford, UC Davis |
| Location: | 2112 MSB |
| Start time: | Thu, Jan 12 2006, 1:10PM |
Description
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.