Smooth knots in a~fibering over a~circumference

S. G. Smirnov

Sbornik. Mathematics, Tome 14 (1971) no. 2, pp. 252-266

Résumé

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.