Handle moves in contact surgery diagrams

2008/05/21 by Fan Ding, Hansjörg Geiges · 3 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #Combinatorics #Computer science #Connective tissue disorders research #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Isotopy #Mathematics #Pure mathematics #Space (punctuation) #math.GT #math.SG #msc:53D10 #msc:57M25 #msc:57R17 #msc:57R65

paper · pdf · doi:10.1112/jtopol/jtp002

published as J. Topol. 2 (2009), 105-122 · 20 pages, 26 figures

arxiv created 2008/05/21 · openalex publication_date 2009/01/01 · arxiv updated 2014/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We describe various handle moves in contact surgery diagrams, notably contact analogues of the Kirby moves. As an application of these handle moves, we discuss the classification of loose Legendrian knots. Along the way, we prove a one-to-one correspondence (up to Legendrian isotopy) between long Legendrian knots in 3-space and their completion in the 3-sphere.

Citations

• Sur les transformations de contact au-dessus des surfaces
• Classification of overtwisted contact structures on 3-manifolds
• Legendrian knots in overtwisted contact structures

Cited by

• Mirror symmetry for the Painlevé character varieties
• Lagrangian slice disks with symplectomorphic exteriors
• Canonical contact structures on some singularity links

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• On A Potential Contact Analogue Of Kirby Move Of Type 1
• Knots and Contact Geometry
• On contact surgery
• Contact Surgeries on the Legendrian Figure-Eight Knot
• Compatible Relative Open Books on Relative Contact Pairs via Generalized Square Bridge Diagrams