New Invariants of Legendrian Knots

  • Yuri Chekanov
Conference paper
Part of the Progress in Mathematics book series (PM, volume 202)


We discuss two different ways to construct new invariants of Legendrian knots in the standard contact R3. These invariants are defined combinatorially, in terms of certain planar projections, and (sometimes) allow us to distinguish Legendrian knots which are not Legendrian isotopic but have the same classical invariants.


Rotation Number Maslov Index Isotopy Class Differential Algebra Classical Invariant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    [] Yu. V. Chekanov, Differential algebra of Legendrian links, to appear.Google Scholar
  2. 2.
    [] Yu. V. Chekanov and P. E. Pushkar, Arnold’s four cusp conjecture and invariants of Legendrian knots, in preparation.Google Scholar
  3. 3.
    Ya. Eliashberg, A theorem on the structure of wave fronts and its application in symplectic topology, Funct. Anal. Appl. 21 1987, 227–232.MathSciNetGoogle Scholar
  4. 4.
    Ya. Eliashberg, Legendrian and transversal knots in tight contact 3-manifolds, In: Topological methods in modern mathematics (Stony Brook, NY, 1991), Publish or Perish, 1993, 171–193.Google Scholar
  5. 5.
    [] Ya. Eliashberg, Invariants in contact topology, In: Proceedings ICM 1998 II, Doc. Math., Extra volume, 327–338.Google Scholar
  6. 6.
    Ya. Eliashberg and M. Fraser, Classification of topologically trivial Legendrian knots, In: Geometry, topology, and dynamics (Montreal, PQ, 1995), CRM Proc. Lecture Notes, 15, AMS, Providence, 1998, 17–51.Google Scholar
  7. 7.
    A. Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys. 120 1989, 575–611.MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    D. Fuchs and S. Tabachnikov, Invariants of Legendrian and transverse knots in the standard contact space, Topology 36 (1997), 1025–1053.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Basel AG 2001

Authors and Affiliations

  • Yuri Chekanov
    • 1
  1. 1.Moscow Center for Continuous Mathematics EducationMoscowRussia

Personalised recommendations