2023/12/14 by Maya Basu, Basu, Maya, Austin Christian +9
Computer Science · Mathematics · #53D42 (Primary) 57K10 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2312.09144
openalex publication_date 2023/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work applies the ideas of persistent homology to the problem of distinguishing Legendrian knots. We develop a persistent version of Legendrian contact homology by filtering the Chekanov-Eliashberg DGA using the action (height) functional. We present an algorithm for assigning heights to a Lagrangian diagram of a Legendrian knot, and we explain how each Legendrian Reidemeister move changes the height of generators of the DGA in a way that is predictable on the level of homology. More precisely, a Reidemeister move that changes an area patch of a Lagrangian diagram by δ will induce a 2δ-interleaving on the persistent Legendrian contact homology, computed before and after the Reidemeister move. Finally, we develop strong Morse inequalities for our persistent Legendrian contact homology.