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Mat. Zametki, 2019, Volume 105, Issue 3, Pages 332–348 (Mi mz11951)  

Asphericity of Groups Defined by Graphs

V. Yu. Bereznyuk

Lomonosov Moscow State University

Abstract: 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-01-00591 А
This work was supported by the Russian Foundation for Basic Research under grant 19-01-00591 A.


DOI: https://doi.org/10.4213/mzm11951

Full text: PDF file (557 kB)
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UDC: 512.543.16
Received: 31.01.2018
Revised: 16.07.2018

Citation: V. Yu. Bereznyuk, “Asphericity of Groups Defined by Graphs”, Mat. Zametki, 105:3 (2019), 332–348

Citation in format AMSBIB
\Bibitem{Ber19}
\by V.~Yu.~Bereznyuk
\paper Asphericity of Groups Defined by Graphs
\jour Mat. Zametki
\yr 2019
\vol 105
\issue 3
\pages 332--348
\mathnet{http://mi.mathnet.ru/mz11951}
\crossref{https://doi.org/10.4213/mzm11951}
\elib{http://elibrary.ru/item.asp?id=37045119}


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