Geodesic
Detecting the Orientation of String Links by Finite Type Invariants
Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 3, pp. 48-59

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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 $\mathfrak{gl}_N$.
Keywords: link, knot, Vassiliev invariant, invertibility. 
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     author = {S. V. Duzhin and M. V. Karev},
     title = {Detecting the {Orientation} of {String} {Links} by {Finite} {Type} {Invariants}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2007_41_3_a3/}
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S. V. Duzhin; M. V. Karev. Detecting the Orientation of String Links by Finite Type Invariants. Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 3, pp. 48-59. http://geodesic.mathdoc.fr/item/FAA_2007_41_3_a3/