Geodesic
Hyperbolicity of one-relator groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 85-102.

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The goal of this work is to understand whether one-relator group $G=\langle a,b|R(a,b)\rangle$, $R(a,b)$ – relator of a special kind, is hyperbolic or not. There were applied combinatorial and geometric methods by S. Ivanov and P. Schupp, based on the use of the diagrams over a group. The result of this work consists of two theorems which classify group $G$ for all the kinds of $R(a,b)$ except two of them. 
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N. V. Buskin. Hyperbolicity of one-relator groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 85-102. http://geodesic.mathdoc.fr/item/SEMR_2007_4_a5/

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