Isomorphism of the groups of Vassiliev Invariants of Legendrian and of Pseudo Legendrian Knots in Contact 3-manifolds

Details Isomorphism of the groups of Vassiliev Invariants of Legendrian and of Pseudo Legendrian Knots in Contact 3-manifolds Isomorphism of the groups of Vassiliev Invariants of Legendrian and of Pseudo Legendrian Knots in Contact 3-manifolds

2000-12-09

arxiv.org/abs/math/0012065v1

Compositio Math. 135 (2003), no. 1, 103--122

Mathematics

Geometric Topology

17 pages, 5 figures

Scientific paper

The study of the Vassiliev invariants of Legendrian knots was started by D. Fuchs and S. Tabachnikov who showed that the groups of complex-valued Vassiliev invariants of Legendrian and of framed knots in the standard contact $R^3$ are canonically isomorphic. Recently we constructed the first examples where Vassiliev invariants of Legendrian and of framed knots are different, and 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.

Affiliated with

Also associated with

No associations

Rating

Isomorphism of the groups of Vassiliev Invariants of Legendrian and of Pseudo Legendrian Knots in Contact 3-manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Isomorphism of the groups of Vassiliev Invariants of Legendrian and of Pseudo Legendrian Knots in Contact 3-manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Isomorphism of the groups of Vassiliev Invariants of Legendrian and of Pseudo Legendrian Knots in Contact 3-manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-686932