Median quasimorphisms on CAT(0) cube complexes and their cup products
arXiv:2209.05811 · doi:10.1007/s10711-023-00870-3
Abstract
Cup products provide a natural approach to access higher bounded cohomology groups. We extend vanishing results on cup products of Brooks quasimorphisms of free groups to cup products of median quasimorphisms, i.e., Brooks-type quasimorphisms of group actions on CAT(0) cube complexes. In particular, we obtain such vanishing results for groups acting on trees and for right-angled Artin groups. Moreover, we outline potential applications of vanishing results for cup products in bounded cohomology.
36 pages, 12 figures; v2: corrected mistake in the first version related to infinite staircases. v3: final version, to appear in Geometriae Dedicata