[Quasimorphismes efficaces sur les groupes d’Artin à angle droit]
Nous construisons des nouvelles familles de quasi-morphismes sur de nombreux groupes agissant sur des complexes cubiques CAT(0). Ces quasi-morphismes ont leur défaut majoré par 12, et sont suffisamment nombreux pour « voir » tous les éléments qui agissent de manière hyperbolique sur le complexe cubique. Nous déduisons que la longueur stable des commutateurs de tous ces éléments est minorée par 1/24.
Les actions pour lesquelles ces résultats sont vérifiés comprennent l’action standard d’un groupe d’Artin à angles droits sur son complexe cubique associé. En particulier, la longueur stable des commutateurs de tout élément non trivial d’un groupe d’Artin à angles droits est minorée par 1/24.
Ces résultats reposent sur de nouveaux outils que nous développons pour étudier les actions de groupes sur des complexes cubiques CAT(0) : l’ensemble caractéristique essentiel et les plongements euclidiens équivariants.
We construct families of quasimorphisms on many groups acting on CAT(0) cube complexes. These quasimorphisms have a uniformly bounded defect of 12, and they “see” all elements that act hyperbolically on the cube complex. We deduce that all such elements have stable commutator length at least 1/24.
The group actions for which these results apply include the standard actions of right-angled Artin groups on their associated CAT(0) cube complexes. In particular, every non-trivial element of a right-angled Artin group has stable commutator length at least 1/24.
These results make use of some new tools that we develop for the study of group actions on CAT(0) cube complexes: the essential characteristic set and equivariant Euclidean embeddings.
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Keywords: quasimorphism, stable commutator length, bounded cohomology, CAT(0) cube complex, right-angled Artin group, median property
Mots-clés : quasimorphisme, longueur stable de commutateurs, cohomologie bornée, complexe cubique CAT(0), groupe d’Artin à angle droit, propriété médiane
Fernós, Talia 1 ; Forester, Max 2 ; Tao, Jing 2
CC-BY-ND 4.0
@article{AIF_2019__69_4_1575_0,
author = {Fern\'os, Talia and Forester, Max and Tao, Jing},
title = {Effective quasimorphisms on right-angled {Artin} groups},
journal = {Annales de l'Institut Fourier},
pages = {1575--1626},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {69},
number = {4},
year = {2019},
doi = {10.5802/aif.3277},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3277/}
}
TY - JOUR AU - Fernós, Talia AU - Forester, Max AU - Tao, Jing TI - Effective quasimorphisms on right-angled Artin groups JO - Annales de l'Institut Fourier PY - 2019 SP - 1575 EP - 1626 VL - 69 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3277/ DO - 10.5802/aif.3277 LA - en ID - AIF_2019__69_4_1575_0 ER -
%0 Journal Article %A Fernós, Talia %A Forester, Max %A Tao, Jing %T Effective quasimorphisms on right-angled Artin groups %J Annales de l'Institut Fourier %D 2019 %P 1575-1626 %V 69 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3277/ %R 10.5802/aif.3277 %G en %F AIF_2019__69_4_1575_0
Fernós, Talia; Forester, Max; Tao, Jing. Effective quasimorphisms on right-angled Artin groups. Annales de l'Institut Fourier, Tome 69 (2019) no. 4, pp. 1575-1626. doi : 10.5802/aif.3277. https://aif.centre-mersenne.org/articles/10.5802/aif.3277/
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