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math.GT1999
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…
math.GT1999
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…
math.GT1999
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…
math.GT1999
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…