It is well known how the linking number and framing can be extracted from the degree 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.
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DOI : 10.5802/afst.1773
Meilhan, Jean-Baptiste 1
CC-BY 4.0
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author = {Meilhan, Jean-Baptiste},
title = {Linking coefficients and the {Kontsevich} integral},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {349--360},
year = {2024},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 33},
number = {2},
doi = {10.5802/afst.1773},
mrnumber = {4806786},
zbl = {07938069},
language = {en},
url = {https://www.numdam.org/articles/10.5802/afst.1773/}
}
TY - JOUR AU - Meilhan, Jean-Baptiste TI - Linking coefficients and the Kontsevich integral JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2024 SP - 349 EP - 360 VL - 33 IS - 2 PB - Université Paul Sabatier, Toulouse UR - https://www.numdam.org/articles/10.5802/afst.1773/ DO - 10.5802/afst.1773 LA - en ID - AFST_2024_6_33_2_349_0 ER -
%0 Journal Article %A Meilhan, Jean-Baptiste %T Linking coefficients and the Kontsevich integral %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2024 %P 349-360 %V 33 %N 2 %I Université Paul Sabatier, Toulouse %U https://www.numdam.org/articles/10.5802/afst.1773/ %R 10.5802/afst.1773 %G en %F AFST_2024_6_33_2_349_0
Meilhan, Jean-Baptiste. Linking coefficients and the Kontsevich integral. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 33 (2024) no. 2, pp. 349-360. doi: 10.5802/afst.1773
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