Asphericity of cubical presentations: the 2-dimensional case

Abstract

We show that under suitable hypotheses, the second homotopy group of the coned-off space associated to a $C(9)$ cubical presentation is trivial, and use this to provide classifying spaces for proper actions for the fundamental groups of many quotients of square complexes admitting such cubical presentations. When the cubical presentations satisfy a condition analogous to requiring that the relators in a group presentation are not proper powers, we conclude that the corresponding coned-off space is aspherical.

24 pages, 1 figure. Implemented referees' comments, accepted for publication at IMRN (section 2 of this document is omitted in the journal version); this version differs from the previous version only in that a reference has been updated

References in corpus (2)

• A metric Kan-Thurston theorem
• Asphericity of cubical presentations: the general case