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Le groupe d'automorphismes du groupe modulaire

Tambekou Roger Tchangang (1987)

Annales de l'institut Fourier

Le but de cet article est de donner une autre démonstration plus simple du théorème d’Ivanov (Théorème 1) qui assure que le groupe $M_{g}^{*}$ de toutes les difféotopies d’une surface $F_{g}$ orientable et fermée de genre $g \geq 2$ est complet. En étudiant l’action d’un automorphisme quelconque du groupe $M_{g}^{*}$ sur les difféotopies d’ordre fini, on montre que les involutions hyperelliptiques sont globalement préservées. Le théorème d’Ivanov est alors une conséquence d’un résultat de Dyer et Grossmann qui affirm que le groupe...

Left-Garside categories, self-distributivity, and braids

Patrick Dehornoy (2009)

Annales mathématiques Blaise Pascal

In connection with the emerging theory of Garside categories, we develop the notions of a left-Garside category and of a locally left-Garside monoid. In this framework, the relationship between the self-distributivity law LD and braids amounts to the result that a certain category associated with LD is a left-Garside category, which projects onto the standard Garside category of braids. This approach leads to a realistic program for establishing the Embedding Conjecture of [Dehornoy, Braids and...

Lifting of homeomorphisms to branched coverings of a disk

Bronisław Wajnryb, Agnieszka Wiśniowska-Wajnryb (2012)

Fundamenta Mathematicae

We consider a simple, possibly disconnected, d-sheeted branched covering π of a closed 2-dimensional disk D by a surface X. The isotopy classes of homeomorphisms of D which are pointwise fixed on the boundary of D and permute the branch values, form the braid group Bₙ, where n is the number of branch values. Some of these homeomorphisms can be lifted to homeomorphisms of X which fix pointwise the fiber over the base point. They form a subgroup $L^{π}$ of finite index in Bₙ. For each equivalence class...

Linear representations of the group of conjugating automorphisms and the braid groups of some manifolds.

Bardakov, V.G. (2005)

Sibirskij Matematicheskij Zhurnal

L'ordre de Dehornoy sur les tresses

Christian Kassel (1999/2000)

Séminaire Bourbaki