Seifert Surfaces, Commutators and Vassiliev Invariants

Regular Seifert Surfaces and Vassiliev Knot Invariants

Finite Type Invariants of Knots via Their Seifert Matrices∗

We define a filtration on the vector space spanned by Seifert matrices of knots related to Vassiliev’s filtration on the space of knots. Further we show that the invariants of knots derived from the filtration can be expressed by coefficients of the Alexander polynomial. The theory of finite type invariants (Vassiliev invariants) for knots was first introduced by V. Vassiliev [13] and reformula...

Vassiliev Homotopy String Link Invariants

We investigate Vassiliev homotopy invariants of string links, and find that in this particular case, most of the questions left unanswered in [3] can be answered affirmatively. In particular, Vassiliev invariants classify string links up to homotopy, and all Vassiliev homotopy string link invariants come from marked surfaces as in [3], using the same construction that in the case of knots gives...

Vassiliev invariants for braids on surfaces

We show that Vassiliev invariants separate braids on a closed oriented surface, and we exhibit an universal Vassiliev invariant for these braids in terms of chord diagrams labeled by elements of the fundamental group of the considered surface. 1 Definitions and statements 1.

Configuration Space Integrals and Universal Vassiliev Invariants over Closed Surfaces

We show the existence of a universal Vassiliev invariant for links in closed surface cylinders by explicit construction using configuration space integrals.