Geodesic
The groups of knotted compact surfaces, and central extensions
Sbornik. Mathematics, Tome 187 (1996) no. 2, pp. 237-257 Cet article a éte moissonné depuis la source Math-Net.Ru

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A homological characterization is given for groups admitting a presentation by means of defining relations of the form $x^{-1}_\alpha x_\beta x_\alpha =x_\gamma ^\varepsilon$ (the $x_*$ are generators, $\varepsilon =\pm 1$). The importance of such groups for geometry is connected with the fact that the finitely presented groups of this class are precisely the groups of knotted compact surfaces in $\mathbb R^4$. 
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Yu. V. Kuz'min. The groups of knotted compact surfaces, and central extensions. Sbornik. Mathematics, Tome 187 (1996) no. 2, pp. 237-257. http://geodesic.mathdoc.fr/item/SM_1996_187_2_a4/

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