Transverse and Legendrian invariants of cables in combinatorial link Floer homology

2019/03/28 by Apratim Chakraborty, Chakraborty, Apratim · 1 citation
Mathematics · Medicine · #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT

paper · pdf · doi:10.48550/arxiv.1903.12256

23 pages, 13 figures; major revision

openalex publication_date 2019/03/28 · arxiv created 2021/10/02 · arxiv updated 2021/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Ozsváth-Szabó-Thurston transverse invariant in combinatorial link Floer homology for certain transverse cables \mathscrL_p,q of transverse link L in S³. Transverse cables \mathscrL_p,q are constructed from the grid diagram of L. The main result is θ(\mathscrL_p,q)=0 if and only if θ(L)=0 for (q)/(p) sufficiently large. We also prove a similar result for invariants of Legendrian knots. Our proof uses an inclusion map i of certain grid complexes associated to L and L_p,q. We use these results to generate many infinite families of examples of Legendrian and transversely non-simple topological link types.

Cited by

• A note on a Geography problem in knot Floer homology

Related

• On the equivalence of Legendrian and transverse invariants in knot Floer homology
• Cabling Legendrian and transverse knots
• On the Legendrian and transverse classification of cablings
• Cable Links, Annuli and Sutured Floer homology
• An invariant of Legendrian and transverse links from open book decompositions of contact 3-manifolds