# Fox pairings and generalized Dehn twists

Gwénaël Massuyeau^{[1]}; Vladimir Turaev^{[2]}

- [1] IRMA, Université de Strasbourg & CNRS 7 rue René Descartes 67084 Strasbourg, France
- [2] Department of Mathematics Indiana University Bloomington IN47405, USA

Annales de l’institut Fourier (2013)

- Volume: 63, Issue: 6, page 2403-2456
- ISSN: 0373-0956

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topMassuyeau, Gwénaël, and Turaev, Vladimir. "Fox pairings and generalized Dehn twists." Annales de l’institut Fourier 63.6 (2013): 2403-2456. <http://eudml.org/doc/275652>.

@article{Massuyeau2013,

abstract = {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.},

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

author = {Massuyeau, Gwénaël, Turaev, Vladimir},

journal = {Annales de l’institut Fourier},

keywords = {surface; mapping class group; Dehn twist; group; Malcev completion; Fox derivative; fundamental group; surface group automorphism; Malcev completion of a group},

language = {eng},

number = {6},

pages = {2403-2456},

publisher = {Association des Annales de l’institut Fourier},

title = {Fox pairings and generalized Dehn twists},

url = {http://eudml.org/doc/275652},

volume = {63},

year = {2013},

}

TY - JOUR

AU - Massuyeau, Gwénaël

AU - Turaev, Vladimir

TI - Fox pairings and generalized Dehn twists

JO - Annales de l’institut Fourier

PY - 2013

PB - Association des Annales de l’institut Fourier

VL - 63

IS - 6

SP - 2403

EP - 2456

AB - 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.

LA - eng

KW - surface; mapping class group; Dehn twist; group; Malcev completion; Fox derivative; fundamental group; surface group automorphism; Malcev completion of a group

UR - http://eudml.org/doc/275652

ER -

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