Median quasimorphisms on CAT(0) cube complexes and their cup products
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jats:titleAbstract</jats:title>jats:pCup 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 jats:inline-formulajats:alternativesjats:tex-math$${{,\mathrm{{CAT}},}}(0)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:mrow <mml:mspace /> mml:miCAT</mml:mi> <mml:mspace /> </mml:mrow> mml:mo(</mml:mo> mml:mn0</mml:mn> mml:mo)</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> 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.</jats:p>
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Acknowledgements: We wish to thank Matthew Cordes, Talia Fernós, Elia Fioravanti and Nicolas Monod for helpful discussions, as well as Sofia Amontova, Michelle Bucher, and Marco Moraschini for discussions on cup products and Lex. Moreover, we would like to thank Franziska Hofmann for spotting a gap in an earlier version of this paper, and the anonymous referee for several helpful comments, including a fix of the gap.
Funder: Herchel Smith Postdoctoral Fellowship Fund
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1572-9168
