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 $\mathbb R^4$.
\Bibitem{Kuz96}
\by Yu.~V.~Kuz'min
\paper The groups of knotted compact surfaces, and central extensions
\jour Sb. Math.
\yr 1996
\vol 187
\issue 2
\pages 237--257
\mathnet{http://mi.mathnet.ru/eng/sm110}
\crossref{https://doi.org/10.1070/SM1996v187n02ABEH000110}
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\zmath{https://zbmath.org/?q=an:0871.57026}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0030306748}
Linking options:
https://www.mathnet.ru/eng/sm110
https://doi.org/10.1070/SM1996v187n02ABEH000110
https://www.mathnet.ru/eng/sm/v187/i2/p81
This publication is cited in the following 6 articles:
Maxim Ivanov, “Non-abelian tensor product and circular orderability of groups”, Topology and its Applications, 2024, 109111
Vik. S. Kulikov, “Alexander modules of irreducible $C$-groups”, Izv. Math., 72:2 (2008), 305–344
Citation in format AMSBIB
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