Median quasimorphisms on CAT(0) cube complexes and their cup products

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.

arXiv comment36 pages, 12 figures; v2: corrected mistake in the first version related to infinite staircases. v3: final version, to appear in Geometriae Dedicata

References in corpus (8)

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• Induced quasi-cocycles on groups with hyperbolically embedded subgroups
• The Median Class and Superrigidity of Actions on CAT(0) Cube Complexes
• Bounded cohomology and binate groups
• Extending higher dimensional quasi-cocycles
• Amenable category and complexity
• Effective quasimorphisms on right-angled Artin groups
• Bounded cohomology of classifying spaces for families of subgroups