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Isomorphism of the groups of Vassiliev Invariants of Legendrian and of Pseudo Legendrian Knots in Contact 3-manifolds
Vladimir Tchernov
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…
The Most Refined Invariant of Degree One of Knots and Links in -Fibrations Over a Surface
Vladimir Tchernov
As it is well-known, all Vassiliev invariants of degree one of a knot are trivial. There are nontrivial Vassiliev invariants of degree one, when the ambient space is…
Arnold-type Invariants of Curves on Surfaces
Vladimir Tchernov
Recently V. Arnold introduced Strangeness and invariants of generic immersions of an oriented circle to . Here these invariants are generalized to the case of gener…
Homotopy Groups of the Space of Curves on a Surface
Vladimir Tchernov
We explicitly calculate the fundamental group of the space of all immersed closed curves on a surface . It is shown that , n>1 for $F\neq S^2, RP…
Shadows of Wave Fronts and Arnold-Bennequin Type Invariants of Fronts on Surfaces and Orbifolds
Vladimir Tchernov
A first order Vassiliev invariant of an oriented knot in an -fibration and a Seifert fibration over a surface is constructed. It takes values in a quotient of the group ring o…
Arnold-type invariants of wave fronts on surfaces
Vladimir V. Tchernov
Recently Arnold's $\St$ and invariants of generic planar curves have been generalized to the case of generic planar wave fronts. We generalize these invariants to the cas…