English

Asphericity of groups defined by graphs

Group Theory 2022-06-17 v2

Abstract

A graph Γ\Gamma labelled by a set SS defines a group G(Γ)G(\Gamma) whose generators are the set of labels SS and whose relations are all words which can be read on closed paths of this graph. We introduce the notion of aspherical graph and prove that such a graph defines an aspherical group presentation. This result generalizes a theorem of Dominik Gruber on graphs satisfying graphical C(6)C(6)-condition and also allows to get new graphical conditions of asphericity analogous to some classical conditions.

Keywords

Cite

@article{arxiv.1711.05293,
  title  = {Asphericity of groups defined by graphs},
  author = {Vadim Bereznyuk},
  journal= {arXiv preprint arXiv:1711.05293},
  year   = {2022}
}
R2 v1 2026-06-22T22:46:02.974Z