CAT(0) cube complexes and asymptotically rigid mapping class groups

The present paper contributes to the study of asymptotically rigid mapping class groups of infinitely punctured surfaces obtained by thickening planar trees. In a paper from 2022, Genevois, Lonjou and Urech study the latter groups using cube complexes. We determine in which cases their cube complexes are CAT(0) From this study, we develop a family of CAT(0) cubes complexes on which the asymptotically rigid mapping class groups act.