By S. Tadachnikoz, Serge Tabachnikov
This e-book provides a set of papers on similar themes: topology of knots and knot-like items (such as curves on surfaces) and topology of Legendrian knots and hyperlinks in three-d touch manifolds. Featured is the paintings of foreign specialists in knot idea ("quantum" knot invariants, knot invariants of finite type), in symplectic and call topology, and in singularity thought. The interaction of various tools from those fields makes this quantity precise within the learn of Legendrian knots and knot-like gadgets reminiscent of wave fronts. a very attractive characteristic of the quantity is its overseas importance. the quantity effectively embodies a good collaborative attempt by way of all over the world specialists from Belgium, France, Germany, Israel, Japan, Poland, Russia, Sweden, the U.K., and the U.S.
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Extra resources for Differential and Symplectic Topology of Knots and Curves
1991 Mathematics Subject Classification. Primary 57M25, Secondary 57R45. Supported by an RDF grant of The University of Liverpool. ©1999 American Mathematical Society 37 38 VICTOR GORYUNOV The approach by Le and Murakami (their regularisation of the Kontsevich integral) works only for the blackboard framing. Unfortunately, this is not sufficient for the study of plane curves. Indeed, the canonical framing of the Legendrian lift of a regular plane curve is blackboard only with respect to the projection which is not very convenient to consider if one wants to construct Vassiliev type theory for plane curves.
It can be shown that this cobordism relation is an equivalence relation between embedded oriented Legendre submanifolds of }vI. The union of submanifolds induces a semi-group structure on the set of Legendre cobordism classes. 1. This semi-group is always a group. The inverse of the Legendre cobordism class of l is the class of -l, the Legendre sub manifold obtained from l by reversing its orientation. ON LEGENDRE COBORDISMS 25 PROOF. ) as the zero section. ) in which its standard contact form is du - pdq.
The invariant J- of plane curves without "safe" self-tangencies defined in [Ar2] is in fact J- = F + 1. 3. Cobordism of wave fronts. , cobordism of wave fronts. 8 ([Arl]). , W is the projection of a generic big Legendre manifold lying in ST*(lR 2 x [0,1]). Furthermore, they are said to be J- -cobordant if none of the slices Wt (t E [0, 1]) features a J- -singularity. The wave fronts of two Legendre cobordant Legendre links of ST*lR2 are cob ordant, but the converse does not hold. The difference consists in the Morse perestroikas (reconstructions) shown in Figure 10, which change the index, but not the Maslov index.
Differential and Symplectic Topology of Knots and Curves by S. Tadachnikoz, Serge Tabachnikov