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Comptes Rendus Mathématique
Volume 348, n° 15-16
pages 923-926 (août 2010)
Doi : 10.1016/j.crma.2010.07.011
Received : 25 June 2010 ;  accepted : 15 July 2010
On the commutator length of a Dehn twist
Sur la longueur des commutateurs d'un twist de Dehn
 

Błażej Szepietowski 1
Institute of Mathematics, Gdańsk University, Wita Stwosza 57, 80-952 Gdańsk, Poland 

Abstract

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.

The full text of this article is available in PDF format.
Résumé

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.

The full text of this article is available in PDF format.
1  Supported by MNiSW grant N N201 366436.


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