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Smooth knots in a manifold of homotopy type $K(\pi,1)$
S. G. Smirnov
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
Citation:
S. G. Smirnov, “Smooth knots in a manifold of homotopy type $K(\pi,1)$”, Math. USSR-Izv., 9:3 (1975), 577–598
Linking options:
https://www.mathnet.ru/eng/im2043https://doi.org/10.1070/IM1975v009n03ABEH001491 https://www.mathnet.ru/eng/im/v39/i3/p610
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Abstract page: | 216 | Russian version PDF: | 77 | English version PDF: | 7 | References: | 60 | First page: | 1 |
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