Abstract:
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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