Fox pairings and generalized Dehn twists
Annales de l'Institut Fourier, Volume 63 (2013) no. 6, pp. 2403-2456.

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.

DOI: 10.5802/aif.2834
Classification: 57M05,  57N05,  20F28,  20F34,  20F38
Keywords: surface, mapping class group, Dehn twist, group, Malcev completion, Fox derivative
Massuyeau, Gwénaël 1; Turaev, Vladimir 2

1 IRMA, Université de Strasbourg & CNRS 7 rue René Descartes 67084 Strasbourg, France
2 Department of Mathematics Indiana University Bloomington IN47405, USA
     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 = {}
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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.

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