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

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 particul...

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Bibliographic Details
Published in:Geometriae dedicata 2024-02, Vol.218 (1)
Main Authors: Brück, Benjamin, Fournier-Facio, Francesco, Löh, Clara
Format: Article
Language:English
Subjects:
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Homology
Hyperbolic Geometry
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Topology
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Summary: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.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-023-00870-3