Bypasses for rectangular diagrams. A proof of the Jones conjecture and related questions

DOI10.1090/S0077-1554-2014-00210-7zbMath1307.57004arXiv1206.0898WikidataQ123150189 ScholiaQ123150189MaRDI QIDQ2930852

M. V. Prasolov, Ivan A. Dynnikov

Publication date: 20 November 2014

Published in: Transactions of the Moscow Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.0898

zbMATH Keywords

Legendrian knotsbypassmonotonic simplificationrectagular link diagramrepresentation of links by braids

Mathematics Subject Classification ID

Related Items (22)

On homogeneous quasipositive links ⋮ Positivities of Knots and Links and the Defect of Bennequin Inequality ⋮ Geography of Legendrian knot mosaics ⋮ On cobordisms between knots, braid index, and the upsilon-invariant ⋮ A quantitative Birman–Menasco finiteness theorem and its application to crossing number ⋮ Low-dimensional topology. Abstracts from the workshop held January 15--21, 2023 ⋮ Distinguishing Legendrian knots with trivial orientation-preserving symmetry group ⋮ A note on knot fertility. II ⋮ Distinguishing Legendrian knots in topological types 74, 948, 10136 with maximal Thurston–Bennequin number ⋮ A description of Rasmussen’s invariant from the divisibility of Lee’s canonical class ⋮ Rectangular diagrams of surfaces: representability ⋮ Operations on open book foliations ⋮ Comparing Bennequin-type inequalities ⋮ Embedded annuli and Jones' conjecture ⋮ Multiflypes of rectangular diagrams of links ⋮ On alternating quasipositive links ⋮ On a relation between the self-linking number and the braid index of closed braids in open books ⋮ Transverse-Legendrian links ⋮ Classification of Legendrian knots of topological type 76 with maximal Thurston–Bennequin number ⋮ Flat plumbing basket and contact structure ⋮ A diagrammatic approach for determining the braid index of alternating links ⋮ Lernaean knots and band surgery

Cites Work

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• Transversal torus knots
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• Embedding knots and links in an open book. I: Basic properties
• Legendrian knots, transverse knots and combinatorial Floer homology
• Seifert circles, braid index and the algebraic crossing number
• ON ARC INDEX AND MAXIMAL THURSTON–BENNEQUIN NUMBER
• Grid Diagrams, Braids, and Contact Geometry
• MARKOV THEOREM FOR TRANSVERSAL LINKS
• Arc-presentations of links: Monotonic simplification

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