2024/09/09 by Milica Dukic, Dukic, Milica
Computer Science · Mathematics · #53D12 #53D42 #57K33 #57R17 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Matrix Theory and Algorithms #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2409.05856
openalex publication_date 2024/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define an SFT-type invariant for Legendrian knots in the standard contact ℝ3. The invariant is a deformation of the Chekanov-Eliashberg differential graded algebra. The differential consists of a part that counts index zero J-holomorphic disks with up to two positive punctures, annuli with one positive puncture, and a string topological part. We describe the invariant and demonstrate its invariance combinatorially from the Lagrangian knot projection, and compute some simple examples where the deformation is non-vanishing.