Median quasimorphisms on $${{\,\mathrm{{CAT}}\,}}(0)$$ cube complexes and their cup products
Median quasimorphisms on $${{\,\mathrm{{CAT}}\,}}(0)$$ 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 $${{\,\mathrm{{CAT}}\,}}(0)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mspace/><mml:mi>CAT</mml:mi><mml:mspace/></mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> cube complexes. In particular, we obtain such vanishing …