Handle moves in contact surgery diagrams

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 respective classifications of long and loose Legendrian knots.

20 pages, 26 figures

References in corpus (2)

• Surgery diagrams for contact 3-manifolds
• Legendrian knots in overtwisted contact structures

Cited by in corpus (18)

• Khovanov homology detects the trefoils
• Planar open books, monodromy factorizations, and symplectic fillings
• Legendrian Fronts for Affine Varieties
• The diffeotopy group of S^1 \times S^2 via contact topology
• Canonical contact structures on some singularity links
• Monopole Floer homology and Legendrian knots
• Dehn Twists in Heegaard Floer Homology
• Contact surgery and supporting open books
• Non-looseness of non-loose knots
• Diagrams for contact 5-manifolds
• Lefschetz Fibrations on Compact Stein Manifolds
• Fillability of small Seifert fibered spaces
• Stein traces and characterizing slopes
• Contact surgery graphs
• Weinstein presentations for high-dimensional antisurgery
• Contact (+1)-surgeries on rational homology 3-spheres
• Exact Lagrangian tori in symplectic Milnor fibers constructed with fillings
• On Contact Round Surgeries on $({\mathbb{S}}^3,{\xi }_{st})$ and Their Diagrams