7 citations · 12 across the 8 of their papers we have counts for
8 papers
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…
Vassiliev invariants of Legendrian, of transverse and framed knots in contact 3-manifolds
Vladimir Tchernov
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 tha…
Finite Order Invariants of Legendrian, Transverse, and Framed Knots in Contact 3-manifolds
Vladimir Tchernov
We show that for a big class of contact manifolds the groups of order invariants (with values in an arbitrary Abelian group) of Legendrian, of transverse and of framed kno…
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…