2019/02/13 by Genevois, Anthony
#20F16 #20F65 #20F67 #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1902.04883
In this article, we associate to isometries of CAT(0) cube complexes specific subspaces, referred to as median sets, which play a similar role as minimising sets of semisimple isometries in CAT(0) spaces. Various applications are deduced, including a cubulation of centralisers, a splitting theorem, a proof that Dehn twists in mapping class groups must be elliptic for every action on a CAT(0) cube complex, a cubical version of the flat torus theorem, and a structural theorem about polycyclic groups acting on CAT(0) cube complexes.