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Mathematics of the USSR-Izvestiya, 1975, Volume 9, Issue 3, Pages 577–598
DOI: https://doi.org/10.1070/IM1975v009n03ABEH001491
(Mi im2043)
 

Smooth knots in a manifold of homotopy type $K(\pi,1)$

S. G. Smirnov
References:
Abstract: The author studies the set $\operatorname{Iso}(S^m,M^n)$ of smooth isotopy classes of embeddings of a sphere $S^m$ in a manifold $M^n$ having homotopy type $K(\pi,1)$, where $1<m<n-2$. He obtains an explicit expression for $\operatorname{Iso}(S^m,M^n)$ in terms of the group $\pi=\pi_1(M^n)$ and the well-known Haefliger groups of knots and finite links of the sphere $S^m$ in $R^n$.
Bibliography: 7 items.
Received: 05.07.1973
Revised: 16.01.1975
Bibliographic databases:
UDC: 513.83
MSC: Primary 57C45; Secondary 57D40
Language: English
Original paper language: Russian
Citation: S. G. Smirnov, “Smooth knots in a manifold of homotopy type $K(\pi,1)$”, Math. USSR-Izv., 9:3 (1975), 577–598
Citation in format AMSBIB
\Bibitem{Smi75}
\by S.~G.~Smirnov
\paper Smooth knots in a~manifold of homotopy type~$K(\pi,1)$
\jour Math. USSR-Izv.
\yr 1975
\vol 9
\issue 3
\pages 577--598
\mathnet{http://mi.mathnet.ru//eng/im2043}
\crossref{https://doi.org/10.1070/IM1975v009n03ABEH001491}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=400248}
\zmath{https://zbmath.org/?q=an:0327.57013}
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  • https://doi.org/10.1070/IM1975v009n03ABEH001491
  • https://www.mathnet.ru/eng/im/v39/i3/p610
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:216
    Russian version PDF:77
    English version PDF:7
    References:60
    First page:1
     
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