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JOURNALS // Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya // Archive

Izv. Akad. Nauk SSSR Ser. Mat., 1975 Volume 39, Issue 3, Pages 610–634 (Mi im2043)

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.

UDC: 513.83

MSC: Primary 57C45; Secondary 57D40

Received: 05.07.1973
Revised: 16.01.1975


 English version:
Mathematics of the USSR-Izvestiya, 1975, 9:3, 577–598

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