Abstract

Abstract 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 ) \operatorname{CAT(0)} . From this study, we develop a family of CAT ⁢ ( 0 ) \operatorname{CAT(0)} cubes complexes on which the asymptotically rigid mapping class groups act.

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