Vassiliev invariants of Legendrian, of transverse and framed knots in contact 3-manifolds

Details Vassiliev invariants of Legendrian, of transverse and framed knots in contact 3-manifolds Vassiliev invariants of Legendrian, of transverse and framed knots in contact 3-manifolds

2000-04-29

arxiv.org/abs/math/0005002v1

Topology 42 (2003), no. 1, 1--33

Mathematics

Symplectic Geometry

32 pages, 7 Figures; This is a continuation of my researh described in math.SG/9907118

Scientific paper

We show that for a large class of contact 3-manifolds the groups of Vassiliev invariants of Legendrian and of framed knots are canonically isomorphic. As a corollary, we obtain that the group of finite order Arnold's $J^+$-type invariants of wave fronts on a surface $F$ is isomorphic to the group of Vassiliev invariants of framed knots in the spherical cotangent bundle $ST^*F$ of $F$. On the other hand we construct the first examples of contact manifolds for which Vassiliev invariants of Legendrian knots can distinguish Legendrian knots that realize isotopic framed knots and are homotopic as Legendrian immersions.

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