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

Published version
Repository DOI

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Authors
Brück, B 
Fournier-Facio, F 
Löh, C 
Abstract

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>

Description

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

Keywords
4904 Pure Mathematics, 49 Mathematical Sciences
Journal Title
Geometriae Dedicata
Conference Name
Journal ISSN
0046-5755
1572-9168
Volume Title
218
Publisher
Springer Science and Business Media LLC
Sponsorship
Deutsche Forschungsgemeinschaft (CRC 1085)