We introduce a notion of a Fox pairing in a group algebra and use Fox pairings to define automorphisms of the Malcev completions of groups. These automorphisms generalize to the algebraic setting the action of the Dehn twists in the group algebras of the fundamental groups of surfaces. This work is inspired by the Kawazumi–Kuno generalization of the Dehn twists to non-simple closed curves on surfaces.
Nous introduisons la notion de “forme de Fox” sur une algèbre de groupe et nous utilisons les formes de Fox pour définir des automorphismes des complétés de Malcev de groupes. Ces automorphismes étendent au cadre algébrique l’action des twists de Dehn sur les algèbres de groupes fondamentaux de surfaces. Ce travail s’inspire de la généralisation des twists de Dehn par Kawazumi–Kuno aux courbes fermées non-simples sur les surfaces.
Keywords: surface, mapping class group, Dehn twist, group, Malcev completion, Fox derivative
Mot clés : surface, groupe de difféotopie, twist de Dehn, groupe, complété de Malcev, dérivation de Fox
Massuyeau, Gwénaël 1; Turaev, Vladimir 2
@article{AIF_2013__63_6_2403_0, author = {Massuyeau, Gw\'ena\"el and Turaev, Vladimir}, title = {Fox pairings and generalized {Dehn} twists}, journal = {Annales de l'Institut Fourier}, pages = {2403--2456}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {63}, number = {6}, year = {2013}, doi = {10.5802/aif.2834}, mrnumber = {3237452}, zbl = {1297.57005}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2834/} }
TY - JOUR AU - Massuyeau, Gwénaël AU - Turaev, Vladimir TI - Fox pairings and generalized Dehn twists JO - Annales de l'Institut Fourier PY - 2013 SP - 2403 EP - 2456 VL - 63 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2834/ DO - 10.5802/aif.2834 LA - en ID - AIF_2013__63_6_2403_0 ER -
%0 Journal Article %A Massuyeau, Gwénaël %A Turaev, Vladimir %T Fox pairings and generalized Dehn twists %J Annales de l'Institut Fourier %D 2013 %P 2403-2456 %V 63 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2834/ %R 10.5802/aif.2834 %G en %F AIF_2013__63_6_2403_0
Massuyeau, Gwénaël; Turaev, Vladimir. Fox pairings and generalized Dehn twists. Annales de l'Institut Fourier, Volume 63 (2013) no. 6, pp. 2403-2456. doi : 10.5802/aif.2834. https://aif.centre-mersenne.org/articles/10.5802/aif.2834/
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