2024/05/08 by Amit Kumar, Kumar, Amit, Jake Murphy +3
Computer Science · Mathematics · #53D10 #57M27 #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2405.04724
openalex publication_date 2024/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It was shown in arXiv:1208.5742 that any smooth knot can be represented by an übercrossing projection, i.e. a knot projection with no crossings aside from a single multi-crossing. We extend this idea to Legendrian knots and investigate übercrossing and petal projections in the front and Lagrangian projections. We show that any Legendrian knot with an übercrossing projection in the front projection is smoothly isotopic to the unknot and we demonstrate how to compute the tb and rotation numbers for petal projections in the Lagrangian projection.