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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb. (N.S.), 1971 Volume 85(127), Number 2(6), Pages 256–271 (Mi sm3204)

This article is cited in 2 papers

Smooth knots in a fibering over a circumference

S. G. Smirnov


Abstract: Let $M^n$ be a smooth manifold without boundary, $1\leqslant k\leqslant n$, and let the filtering $M^n = F^n\supset F^{n-1}\supset\dots\supset F^{n-k}=R^{n-k}$ be such that $F^i\subset F^{i+1}$ for each $i$ is an imbedding of a layer in a smooth fibering over $S^1$. In the paper we have obtained an explicit classification of the smooth knots of the sphere $S^m$ in such a manifold $M^n$ under the conditions $m>2$, $n-m>2$.
Bibliography: 10 titles.

UDC: 513.83

MSC: Primary 57C45; Secondary 57A35

Received: 03.06.1970


 English version:
Mathematics of the USSR-Sbornik, 1971, 14:2, 252–266

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