The N-copy of a topologically trivial Legendrian knot
J. Symplectic Geom., Tome 1 (2002) no. 2, p. 659-828 / Harvested from Project Euclid
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We consider Legendrian knots and links in the standard 3-dimensional contact space. In 1997 Chekanov [Ch] introduced a new invariant for these knots. At the same time, a similar construction was suggested by Eliashberg [E1] within the framework of his joing work with Hofer and Givernthal on Symplectic Field Theory ([E2],[EGH]). To a knot diagram, they associated a differential algebra A. Its stable isomorphism type is invariant under Legendrian isotopy of the knot. ¶ In this paper, we introduce an additional structure on this algebra in the case of a Legendrian link. For a link of N components, we show that its algebra splits A = ⊕g ∈ G Ag Here G is a free group on (N - 1) variables. The splitting is determined by the order of the knots and is preserved by the differential. It gives a tool to show that some permutations of link components are impossible to produce by Legendrian isotopy.
Publié le : 2002-12-14
Classification:  
@article{1092749564,
     author = {Mishachev
, K.},
     title = {The N-copy of a topologically trivial Legendrian knot},
     journal = {J. Symplectic Geom.},
     volume = {1},
     number = {2},
     year = {2002},
     pages = { 659-828},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1092749564}
}

Mishachev
, K. The N-copy of a topologically trivial Legendrian knot. J. Symplectic Geom., Tome 1 (2002) no. 2, pp.  659-828. http://gdmltest.u-ga.fr/item/1092749564/