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Sbornik: Mathematics, 1996, Volume 187, Issue 2, Pages 237–257
DOI: https://doi.org/10.1070/SM1996v187n02ABEH000110
(Mi sm110)
 

This article is cited in 6 scientific papers (total in 6 papers)

The groups of knotted compact surfaces, and central extensions

Yu. V. Kuz'min

Moscow State University of Transportation
References:
Abstract: A homological characterization is given for groups admitting a presentation by means of defining relations of the form x1αxβxα=xεγx1αxβxα=xεγ (the xx 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.
Received: 22.06.1995
Bibliographic databases:
UDC: 512.04
MSC: Primary 57Q45, 20F05, 20J05; Secondary 57M25, 53A05, 20K35
Language: English
Original paper language: Russian
Citation: Yu. V. Kuz'min, “The groups of knotted compact surfaces, and central extensions”, Sb. Math., 187:2 (1996), 237–257
Citation in format AMSBIB
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\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
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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:
    1. Maxim Ivanov, “Non-abelian tensor product and circular orderability of groups”, Topology and its Applications, 2024, 109111  crossref
    2. Vik. S. Kulikov, “Alexander modules of irreducible C-groups”, Izv. Math., 72:2 (2008), 305–344  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Vik. S. Kulikov, “Hurwitz curves”, Russian Math. Surveys, 62:6 (2007), 1043–1119  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Yu. Kuzmin, “On solvable groups of knotted surfaces”, J Math Sci, 100:1 (2000), 1877  crossref
    5. V. S. Guba, M. V. Sapir, “On subgroups of R. Thompson's group F and other diagram groups”, Sb. Math., 190:8 (1999), 1077–1130  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. Yu. S. Semenov, “Commutator subgroups of irreducible C-group”, Sb. Math., 187:3 (1996), 403–412  mathnet  crossref  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:379
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    English version PDF:28
    References:53
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