University of Arkansas Topology Seminar: 9/26/2013

Speaker: Dan Rutherford

Title: Rulings polynomials and augmentations into finite fields

Abstract: A normal ruling is a type of decomposition of the front diagram of a Legendrian knot in ℝ3. Making a refined count of normal rulings allows for the definition of a Legendrian link invariant known as the ruling polynomial that is a Laurent polynomial in a variable, z. Another class of Legendrian invariants, the augmentation numbers, arise from making normalized counts of augmentations of the Legendrian contact homology DGA into finite fields. We show that augmentation numbers are determined by specializing the ruling polynomial via z = q½q−½ where q denotes the order of the corresponding finite field. As a corollary, we deduce that the ruling polynomial is determined by the Legendrian contact homology DGA. This is joint work with Brad Henry.