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Mat. Sb. (N.S.), 1981, Volume 115(157), Number 2(6), Pages 223–262 (Mi msb2383)  

This article is cited in 5 scientific papers (total in 5 papers)

Classification of stable fibered knots

M. Sh. Farber


Abstract: In this paper a new invariant of fibered knots is studied, represented as a homotopy pairing in the sense of Spanier and Whitehead. With its help, first of all, a classification of stable fibered knots is given; second, it is shown that certain well-known invariants in knot theory define the type of a stable knot up to a finite number of possibilities; and third, a complete algebraic description of certain classes of knots is given.
Figures: 3.
Bibliography: 33 titles.

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English version:
Mathematics of the USSR-Sbornik, 1982, 43:2, 199–234

Bibliographic databases:

UDC: 513.836
MSC: Primary 57Q45; Secondary 55R55
Received: 15.08.1980

Citation: M. Sh. Farber, “Classification of stable fibered knots”, Mat. Sb. (N.S.), 115(157):2(6) (1981), 223–262; Math. USSR-Sb., 43:2 (1982), 199–234

Citation in format AMSBIB
\Bibitem{Far81}
\by M.~Sh.~Farber
\paper Classification of stable fibered knots
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 115(157)
\issue 2(6)
\pages 223--262
\mathnet{http://mi.mathnet.ru/msb2383}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=622146}
\zmath{https://zbmath.org/?q=an:0494.57010|0483.57013}
\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 43
\issue 2
\pages 199--234
\crossref{https://doi.org/10.1070/SM1982v043n02ABEH002445}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. Sh. Farber, “The classification of simple knots”, Russian Math. Surveys, 38:5 (1983), 63–117  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Farber M., “Knots and Stable-Homotopy”, 1060, 1984, 140–150  mathscinet  zmath  isi
    3. Farber M., “An Algebraic Classification of Some Even-Dimensional Spherical Knots .1.”, Trans. Am. Math. Soc., 281:2 (1984), 507–527  crossref  mathscinet  zmath  isi
    4. Farber M., “Mappings Into a Circle with the Minimal Number of Critical-Points and the Multidimensional Knots”, 279, no. 1, 1984, 43–46  mathscinet  zmath  isi
    5. M. Farber, “Minimal Seifert manifolds and the knot finiteness theorem”, Isr J Math, 66:1-3 (1989), 179  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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