[Longueur stable des commutateurs sur les groupes modulaires des surfaces]
Soit un sous-groupe d’indice fini du groupe modulaire d’une surface fermée orientable, possiblement épointée. Nous donnons une condition précise (en termes de la décomposition de Nielsen-Thurston) pour qu’un élément ait une longueur stable des commutateurs strictement positive. Nous montrons de plus que dans ces situations, la longueur stable des commutateurs est soit nulle, soit uniformément minorée par un réel strictement positif. Notre méthode permet aussi de traiter le cas de certains sous-groupes d’indice infini, et nous montrons l’existence d’un minorant strictement positif pour la longueur stable des commutateurs des éléments non triviaux du groupe de Torelli. Les démonstrations utilisent notre prééédente construction d’actions de groupes sur des quasi-arbres.
Let be a finite index subgroup of the mapping class group of a closed orientable surface , possibly with punctures. We give a precise condition (in terms of the Nielsen-Thurston decomposition) when an element has positive stable commutator length. In addition, we show that in these situations the stable commutator length, if nonzero, is uniformly bounded away from 0. The method works for certain subgroups of infinite index as well and we show is uniformly positive on the nontrivial elements of the Torelli group. The proofs use our previous construction of group actions on quasi-trees.
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Keywords: stable commutator length, mapping class groups, quasi-morphisms, projection complex
Mot clés : Longueur stable des commutateurs
Bestvina, Mladen 1 ; Bromberg, Ken 1 ; Fujiwara, Koji 2
@article{AIF_2016__66_3_871_0,
author = {Bestvina, Mladen and Bromberg, Ken and Fujiwara, Koji},
title = {Stable commutator length on mapping class groups},
journal = {Annales de l'Institut Fourier},
pages = {871--898},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {66},
number = {3},
year = {2016},
doi = {10.5802/aif.3028},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3028/}
}
TY - JOUR AU - Bestvina, Mladen AU - Bromberg, Ken AU - Fujiwara, Koji TI - Stable commutator length on mapping class groups JO - Annales de l'Institut Fourier PY - 2016 SP - 871 EP - 898 VL - 66 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3028/ DO - 10.5802/aif.3028 LA - en ID - AIF_2016__66_3_871_0 ER -
%0 Journal Article %A Bestvina, Mladen %A Bromberg, Ken %A Fujiwara, Koji %T Stable commutator length on mapping class groups %J Annales de l'Institut Fourier %D 2016 %P 871-898 %V 66 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3028/ %R 10.5802/aif.3028 %G en %F AIF_2016__66_3_871_0
Bestvina, Mladen; Bromberg, Ken; Fujiwara, Koji. Stable commutator length on mapping class groups. Annales de l'Institut Fourier, Tome 66 (2016) no. 3, pp. 871-898. doi : 10.5802/aif.3028. https://aif.centre-mersenne.org/articles/10.5802/aif.3028/
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