Fox pairings and generalized Dehn twists

Gwenael Massuyeau (1) , Vladimir Turaev (1, 2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 Department of Mathematics at Indiana University

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.

Domaines: Topologie géométrique [math.GT]; Topologie algébrique [math.AT]

Gwenael Massuyeau, Vladimir Turaev. Fox pairings and generalized Dehn twists. Annales de l'Institut Fourier, 2013, 63 (6), pp.2403-2456. ⟨10.5802/aif.2834⟩. ⟨hal-00626759⟩