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A study of augmentation varieties associated to Legendrian knots/tangles
Student-Run Geometry/Topology Seminar| Speaker: | Tao Su, UC Berkeley |
| Related Webpage: | https://math.berkeley.edu/~taosu/ |
| Location: | 2112 MSB |
| Start time: | Thu, May 24 2018, 2:10PM |
We give a tangle approach in the study of Legendrian knots in contact three-space. This includes Legendrian isotopy invariants: ruling polynomials, and Chekanov-Eliashberg or Legendrian Contact Homology differential graded algebras (LCH DGAs) for Legendrian tangles, generalizing those of Legendrian knots.
By studying the "representation varieties (of rank 1)" of the LCH DGAs, called augmentation varieties, we also see that the points-counting/weight (or virtual Poincare) polynomials of the varieties give the ruling polynomials. The tangle approach in particular provides a generalization and a more natural proof to some previous known results of M.Henry and D.Rutherford.
Time permitting, I will also mention some more aspects of the study of augmentation varieties.