Legendrian Non-simple Whitehead Doubles Of The Trefoil

2025/12/17 by Kıvanç, Saliha
Mathematics · #57K10 #57K18 #57R58 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2512.15914

openalex publication_date 2025/12/17 · openalex created_date 2025/12/21 · openalex updated_date 2026/07/28

Abstract

Ozsváth and Stipsicz showed that some Eliashberg-Chekanov twist knots, which are Whitehead doubles of the unknot, are not Legendrian simple. We extend their result by considering some Whitehead doubles of the trefoil: Using properties of knot Floer homology and the distinguished surgery triangle, we show that this family of knots is Legendrian non-simple in the standard contact 3-sphere.

Citations

• An overview of knot Floer homology
• Naturality and mapping class groups in Heegaard Floer homology
• Contact surgeries and the transverse invariant in knot Floer homology
• Heegaard Floer invariants of Legendrian knots in contact three--manifolds
• Floer homology and knot complements
• Holomorphic disks and knot invariants
• Holomorphic disks and topological invariants for closed three-manifolds
• Holomorphic disks and topological invariants for closed three-manifolds

Related

• Non-Simple knots in Contact 3-Manifolds
• Conjectures on the Khovanov Homology of Legendrian and Transversely Simple Knots
• Legendrian satellites
• Knots and Contact Geometry
• Negative contact surgery on Legendrian non-simple knots