2010/03/18 by Joan E. Licata, Licata, Joan E.
Engineering · Mathematics · Physics and Astronomy · #53D10 #53D42 #57M27 #57M50 #Diagram #Differential (mechanical device) #Engineering #FOS: Mathematics #Finite type invariant #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry #Grid #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Invariant polynomial #Knot (papermaking) #Lagrangian #Lens space #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Polynomial #Pure mathematics #Statistics #Symplectic Geometry (math.SG) #math.GT #math.SG #msc:53D10 #msc:53D42 #msc:57M27 #msc:57M50
paper · pdf · doi:10.48550/arxiv.1003.3685
21 pages, 13 figures, to appear in the Proceedings of the Heidelberg Knot Theory Semester
arxiv created 2010/03/18 · openalex publication_date 2010/03/18 · arxiv updated 2010/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
In this article we study the differential graded algebra (DGA) invariant associated to Legendrian knots in tight lens spaces. Given a grid number one diagram for a knot in L(p, q), we show how to construct a special Lagrangian diagram suitable for computing the DGA invariant for the Legendrian knot specified by the diagram. We then specialize to L(p, p - 1) and show that for two families of knots, the existence of an augmentation of the DGA depends solely on the value of p.