2015/08/21 by David Gay, Gay, David T., Joan E. Licata +1
Computer Science · Mathematics · #57M50 (Secondary) #57R17 (Primary) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1508.05307
openalex publication_date 2015/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use parameterized Morse theory on the pages of an open book decomposition to efficiently encode the contact topology in terms of a labelled graph on a disjoint union of tori (one per binding component). This construction allows us to generalize the notion of the front projection of a Legendrian knot from the standard contact ℝ3 to arbitrary closed contact 3-manifolds. We describe a complete set of moves on such front diagrams, extending the standard Legendrian Reidemeister moves, and we give a combinatorial formula to compute the Thurston-Bennequin number of a nullhomologous Legendrian knot from its front projection.