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Linking coefficients and the Kontsevich integral
Jean-Baptiste Meilhan1
1 Univ. Grenoble Alpes, CNRS, IF, 38000 Grenoble, France
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 33 (2024) no. 2, pp. 349-360.

It is well known how the linking number and framing can be extracted from the degree 1 part of the (framed) Kontsevich integral. This note gives a general formula expressing any product of powers of these two invariants as combination of coefficients in the Kontsevich integral. This allows in particular to express the sum of all coefficients of a given degree in terms of the linking coefficients. The proofs are purely combinatorial.

Il est bien connu que l’enlacement et l’auto-enlacement peuvent être extraits de la partie de degré 1 de l’intégrale de Kontsevich (parallélisée). Cette note donne une formule générale, exprimant tout produit de puissances de ces deux invariants comme combinaison de coefficients dans l’intégrale de Kontsevich. Ceci permet en particulier d’exprimer la somme de tous les coefficients en un degré donné en termes de la matrice d’enlacement. Les preuves sont purement combinatoires.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1773
Keywords: Kontsevich integral, Jacobi diagrams, linking number, framing

Jean-Baptiste Meilhan 1

1 Univ. Grenoble Alpes, CNRS, IF, 38000 Grenoble, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Jean-Baptiste Meilhan. Linking coefficients and the Kontsevich integral. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 33 (2024) no. 2, pp. 349-360. doi : 10.5802/afst.1773. https://afst.centre-mersenne.org/articles/10.5802/afst.1773/

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