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

Abstract

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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.

How to cite

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Massuyeau, 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 -

References

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  14. C. D. Papakyriakopoulos, Planar regular coverings of orientable closed surfaces, Knots, groups, and 3-manifolds (Papers dedicated to the memory of R. H. Fox) (1975), 261-292, Princeton Univ. Press, Princeton, N.J. Zbl0325.55002MR388396
  15. B. Perron, A homotopic intersection theory on surfaces: applications to mapping class group and braids, Enseign. Math. (2) 52 (2006), 159-186 Zbl1161.57009MR2255532
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