Department of Mathematics

Seminar in Cluster algebras

  •  Dan Rutherford, Ball State University
  •  Normal rulings and augmentation varieties
  •  11/05/2019
  •  3:00 PM - 4:00 PM
  •  C204A Wells Hall

Normal rulings are combinatorial structures associated to the front diagrams of 1-dimensional Legendrian knots in R^3. They were introduced independently by Fuchs and Chekanov-Pushkar in the context of augmentations of the Legendrian DG-algebra and generating families. In this talk I will present joint work with B. Henry in which we construct a decomposition of the augmentation variety into disjoint pieces indexed by normal rulings. The pieces of the decomposition are products of algebraic tori and affine spaces with dimensions determined by the combinatorics of the ruling. As a consequence, the ruling polynomial invariants of Chekanov-Pushkar are seen to be equivalent to augmentation number invariants defined by counting augmentations to finite fields. The construction of the decomposition is based on considering Morse complex sequences which are combinatorial analogs of generating families.



Department of Mathematics
Michigan State University
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