THE CONORMAL TORUS IS A COMPLETE KNOT INVARIANT

DOI10.1017/fmp.2019.1zbMath1426.57021arXiv1604.03520OpenAlexW2337297716WikidataQ127320378 ScholiaQ127320378MaRDI QIDQ5232462

Vivek Shende

Publication date: 12 September 2019

Published in: Forum of Mathematics, Pi (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.03520

zbMATH Keywords

microlocal sheaf theoryisotopic knotLegendrian isotopic conormal tori

Mathematics Subject Classification ID

Symplectic and contact topology in high or arbitrary dimension (57R17) Sheaf cohomology in algebraic topology (55N30) Knot theory (57K10)

Related Items

Lagrangian cobordism functor in microlocal sheaf theory I ⋮ Knot contact homology detects cabled, composite, and torus knots ⋮ Wrapped sheaves ⋮ A complete knot invariant from contact homology ⋮ Legendrian weaves: \(N\)-graph calculus, flag moduli and applications ⋮ Perverse sheaves and knot contact homology ⋮ Knot contact homology, string topology, and the cord algebra ⋮ Sheaves via augmentations of Legendrian surfaces

Cites Work

• Unnamed Item
• Unnamed Item
• Sheaf quantization of Hamiltonian isotopies and applications to nondisplaceability problems
• Legendrian knots and constructible sheaves
• Nonsqueezing property of contact balls
• Perverse sheaves and knot contact homology
• Some global properties of contact structures
• Microlocal branes are constructible sheaves
• Simple homotopy equivalence of nearby Lagrangians
• A complete knot invariant from contact homology
• KCH representations, augmentations, and \(A\)-polynomials
• Nearby Lagrangians with vanishing Maslov class are homotopy equivalent
• Knot contact homology, string topology, and the cord algebra
• Cluster varieties from Legendrian knots
• Framed knot contact homology
• Exact Lagrangian submanifolds in simply-connected cotangent bundles
• On irreducible 3-manifolds which are sufficiently large
• On manifolds all of whose geodesics are closed
• Reconstruction of a variety from the derived category and groups of autoequivalences
• Knot contact homology and representations of knot groups
• Knots are Determined by Their Complements
• Knot contact homology detects cabled, composite, and torus knots
• Derived categories of coherent sheaves and equivalences between them
• Hilbert Space Extremal Problems with Constraints
• A counterexample to the isomorphism problem for integral group rings