Tchernov, V (2003). Isomorphism of the groups of Vassiliev invariants of Legendrian and pseudo-Legendrian knots. Compositio Mathematica, 135(1):103-122.
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The study of the Vassiliev invariants of Legendrian knots was started by D. Fuchs and S. Tabachnikov who showed that the groups of C-valued Vassiliev invariants of Legendrian and of framed knots in the standard contact R3 are canonically isomorphic. Recently we constructed the first examples of contact 3-manifolds where Vassiliev invariants of Legendrian and of framed knots are different. Moreover in these examples Vassiliev invariants of Legendrian knots distinguish Legendrian knots that are isotopic as framed knots and homotopic as Legendrian immersions. This raised the question what information about Legendrian knots can be captured using Vassiliev invariants. Here we answer this question by showing that for any contact 3-manifold with a cooriented contact structure the groups of Vassiliev invariants of Legendrian knots and of knots that are nowhere tangent to a vector field that coorients the contact structure are canonically isomorphic.
|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Uncontrolled Keywords:||contact manifolds; knots; Vassiliev invariants|
|Deposited On:||29 Nov 2010 17:26|
|Last Modified:||23 Nov 2012 14:43|
|Publisher:||London Mathematical Society|
|Free access at:||Publisher DOI. An embargo period may apply.|
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