Asphericity of cubical presentations: the 2-dimensional case
Group Theory
2023-10-31 v3 Geometric Topology
Abstract
We show that under suitable hypotheses, the second homotopy group of the coned-off space associated to a 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.
Cite
@article{arxiv.2305.06296,
title = {Asphericity of cubical presentations: the 2-dimensional case},
author = {Macarena Arenas},
journal= {arXiv preprint arXiv:2305.06296},
year = {2023}
}
Comments
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