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arXiv · 1711.05293

Asphericity of groups defined by graphs

Vadim Bereznyuk
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Abstract

A graph $\Gamma$ labelled by a set $S$ defines a group $G(\Gamma)$ whose generators are the set of labels $S$ 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 $C(6)$-condition and also allows to get new graphical conditions of asphericity analogous to some classical conditions.

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Vadim Bereznyuk. 2017-11-14. Asphericity of groups defined by graphs. https://doi.org/10.1134/s0001434619030027

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