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.
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.
Accepted:
Published online:
Błażej Szepietowski 1
@article{CRMATH_2010__348_15-16_923_0, author = {B{\l}a\.zej Szepietowski}, title = {On the commutator length of a {Dehn} twist}, journal = {Comptes Rendus. Math\'ematique}, pages = {923--926}, publisher = {Elsevier}, volume = {348}, number = {15-16}, year = {2010}, doi = {10.1016/j.crma.2010.07.011}, language = {en}, }
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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