Effective quasimorphisms on right-angled Artin groups
arXiv:1602.05637
Abstract
We construct new 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.
arXiv commentv1: 38 pages, 5 figures. v2: 40 pages, 6 figures. Minor revisions were made, and an error in the proof of Proposition 3.20 has been fixed. To appear in Annales de l'Institut Fourier