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arXiv · 2209.05811

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

Benjamin Brück·Francesco Fournier-Facio·Clara Loeh
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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.

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Benjamin Brück, Francesco Fournier-Facio, Clara Loeh. 2022-09-13. Median quasimorphisms on CAT(0) cube complexes and their cup products. https://doi.org/10.1007/s10711-023-00870-3

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