Geodesic
Asphericity of Groups Defined by Graphs
Matematičeskie zametki, Tome 105 (2019) no. 3, pp. 332-348

Voir la notice de l'article provenant de la source Math-Net.Ru

A graph $\Gamma$ labeled by a set $S$ defines a group $G(\Gamma)$ whose set of generators is the set $S$ of labels and whose relations are all words which can be read on closed paths of this graph. We introduce the notion of an aspherical graph and prove that such a graph defines an aspherical group presentation. This result generalizes a theorem of Dominik Gruber on graphs satisfying the graphical $C(6)$-condition and makes it possible to obtain new graphical conditions of asphericity similar to some classical conditions.
Keywords: asphericity, graphical small cancellation theory. 
@article{MZM_2019_105_3_a1,
     author = {V. Yu. Bereznyuk},
     title = {Asphericity of {Groups} {Defined} by {Graphs}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {332--348},
     publisher = {mathdoc},
     volume = {105},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_3_a1/}
}
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V. Yu. Bereznyuk. Asphericity of Groups Defined by Graphs. Matematičeskie zametki, Tome 105 (2019) no. 3, pp. 332-348. http://geodesic.mathdoc.fr/item/MZM_2019_105_3_a1/