Massuyeau, Gwénaël; Turaev, Vladimir
Fox pairings and generalized Dehn twists  [ Formes de Fox et twists de Dehn généralisés ]
Annales de l'institut Fourier, Tome 63 (2013) no. 6 , p. 2403-2456
MR 3237452 | Zbl 1297.57005 | 1 citation dans Numdam
doi : 10.5802/aif.2834
URL stable : http://www.numdam.org/item?id=AIF_2013__63_6_2403_0

Classification:  57M05,  57N05,  20F28,  20F34,  20F38
Mots clés: surface, groupe de difféotopie, twist de Dehn, groupe, complété de Malcev, dérivation de Fox
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.
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.

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