Abstract:
A homological characterization is given for groups admitting a presentation by means of defining relations of the form x−1αxβxα=xεγx−1αxβxα=xεγ (the x∗x∗ are generators, ε=±1ε=±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 R4.
\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}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1392843}
\zmath{https://zbmath.org/?q=an:0871.57026}
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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