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/}
}
TY  - JOUR
AU  - V. Yu. Bereznyuk
TI  - Asphericity of Groups Defined by Graphs
JO  - Matematičeskie zametki
PY  - 2019
SP  - 332
EP  - 348
VL  - 105
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2019_105_3_a1/
LA  - ru
ID  - MZM_2019_105_3_a1
ER  - 
%0 Journal Article
%A V. Yu. Bereznyuk
%T Asphericity of Groups Defined by Graphs
%J Matematičeskie zametki
%D 2019
%P 332-348
%V 105
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2019_105_3_a1/
%G ru
%F MZM_2019_105_3_a1
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/

[1] I. M. Chiswell, D. J. Collins, J. Huebschmann, “Aspherical group presentations”, Math. Z., 178:1 (1981), 1–36 | DOI | MR | Zbl

[2] M. Gromov, “Random walk in random groups”, Geom. Funct. Anal., 13:1 (2003), 73–146 | DOI | MR | Zbl

[3] Y. Ollivier, “On a small cancellation theorem of Gromov”, Bull. Belg. Math. Soc. Simon Stevin, 13:1 (2006), 75–89 | MR | Zbl

[4] D. Gruber, “Groups with graphical $C(6)$ and $C(7)$ small cancellation presentations”, Trans. Amer. Math. Soc., 367:3 (2015), 2051–2078 | DOI | MR | Zbl

[5] A. A. Klyachko, “A funny property of a sphere and equations over groups”, Comm. Algebra, 21:7 (1993), 2555–2575 | DOI | MR | Zbl

[6] D. J. Collins, J. Huebschmann, “Spherical diagrams and identities among relations”, Math. Ann., 261:2 (1982), 155–183 | DOI | MR | Zbl

[7] R. Lindon, P. Shupp, Kombinatornaya teoriya grupp, Mir, M., 1980 | MR | Zbl