Geodesic
Smooth knots in a fibering over a circumference
Sbornik. Mathematics, Tome 14 (1971) no. 2, pp. 252-266 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{SM_1971_14_2_a5,
     author = {S. G. Smirnov},
     title = {Smooth knots in a~fibering over a~circumference},
     journal = {Sbornik. Mathematics},
     pages = {252--266},
     year = {1971},
     volume = {14},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1971_14_2_a5/}
}
TY  - JOUR
AU  - S. G. Smirnov
TI  - Smooth knots in a fibering over a circumference
JO  - Sbornik. Mathematics
PY  - 1971
SP  - 252
EP  - 266
VL  - 14
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1971_14_2_a5/
LA  - en
ID  - SM_1971_14_2_a5
ER  - 
%0 Journal Article
%A S. G. Smirnov
%T Smooth knots in a fibering over a circumference
%J Sbornik. Mathematics
%D 1971
%P 252-266
%V 14
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1971_14_2_a5/
%G en
%F SM_1971_14_2_a5
S. G. Smirnov. Smooth knots in a fibering over a circumference. Sbornik. Mathematics, Tome 14 (1971) no. 2, pp. 252-266. http://geodesic.mathdoc.fr/item/SM_1971_14_2_a5/

[1] S. Smeil, “O stroenii mnogoobrazii”, Matematika, 8:4 (1964), 95–108

[2] S. G. Smirnov, “Gladkie uzly v mnogoobrazii gomotopicheskogo tipa sfery”, DAN SSSR, 183:5 (1968), 1016–1019 | MR | Zbl

[3] V. L. Golo, “Ob odnom invariante otkrytykh mnogoobrazii”, Izv. AN. SSSR, seriya matem., 31 (1967), 1091–1104 | MR | Zbl

[4] F. T. Farrell, “The obstruction to fibering a manifold over a circle”, Bull. Amer. Math. Soc., 73:5 (1967), 737–740 | DOI | MR | Zbl

[5] J. F. P. Hudson, “Concordance and isotopy of $PL$ embeddings”, Bull. Amer. Math. Soc., 72:5 (1966), 534–535 | DOI | MR | Zbl

[6] A. Haefliger, “Knotted spheres and related geometric problems”, Trudy mezhdunar. kongressa matematikov, Nauka, Moskva, 1968, 437–445 | MR

[7] A. Haefliger, “Enlancements de spheres en codimension supériore à $2$”, Comm. Math. Helv., 41:1 (1966), 51–72 | DOI | MR | Zbl

[8] A. Haefliger, “Differentiable embeddings of $S^n$ in $S^{n+q}$ for $q>2$”, Ann. Math., 83:3 (1966), 402–436 | DOI | MR | Zbl

[9] E. C. Zeeman, Seminar on combinatorial topology, no. 8, Coventry, 1966

[10] D. D. J. Hacon, “Knotted spheres in tori”, Quart. J. Math., 20:80 (1969), 431–445 | DOI | MR