Functional Analysis and Its Applications

, Volume 41, Issue 3, pp 208–216 | Cite as

Detecting the orientation of string links by finite type invariants

  • S. V. Duzhin
  • M. V. Karev
Article
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Abstract

We prove the existence of a degree 7 Vassiliev invariant of long (string) links with two numbered components which is not preserved under orientation reversal. The proof is based on the study of a weight system with values in the tensor square of the universal enveloping algebra for the Lie algebra \(\mathfrak{g}\mathfrak{l}_N \).

Key words

link knot Vassiliev invariant invertibility 
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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • S. V. Duzhin
    • 1
  • M. V. Karev
    • 1
  1. 1.St. Petersburg Division of the Steklov Mathematical InstituteRussia

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