Comptes Rendus
no. 15-16
Topology
On the commutator length of a Dehn twist
[Sur la longueur des commutateurs d'un twist de Dehn]

Présenté par : Étienne Ghys

Błażej Szepietowski1
1 Institute of Mathematics, Gdańsk University, Wita Stwosza 57, 80-952 Gdańsk, Poland
Comptes Rendus. Mathématique, Volume 348 (2010) no. 15-16, pp. 923-926.

Nous démontrons que sur une surface non orientable de genre au moins 7 toute puissance d'un twist de Dehn est égale à un unique commutateur dans le groupe de difféotopies et que ceci est vrai, sous conditions additionnelles, pour le sous-groupe généré par les twists, aussi bien que pour l'extension du groupe de difféotopies d'une surface orientable de genre au moins 3.

We show that on a nonorientable surface of genus at least 7 any power of a Dehn twist is equal to a single commutator in the mapping class group and the same is true, under additional assumptions, for the twist subgroup, and also for the extended mapping class group of an orientable surface of genus at least 3.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.07.011
Błażej Szepietowski 1

1 Institute of Mathematics, Gdańsk University, Wita Stwosza 57, 80-952 Gdańsk, Poland 
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Błażej Szepietowski. On the commutator length of a Dehn twist. Comptes Rendus. Mathématique, Volume 348 (2010) no. 15-16, pp. 923-926. doi : 10.1016/j.crma.2010.07.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.07.011/

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