Geodesic
Local knotting of submanifolds
Sbornik. Mathematics, Tome 19 (1973) no. 2, pp. 166-176 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper the author investigates the modification of the fundamental group of the complement of a submanifold of codimension 2 by knotting in a neighborhood of one of its points. With the aid of such knotting he constructs closed nonorientable surfaces in $\mathbf R^4$ with finite noncommutative groups. In the appendix he constructs a nontrivial knot such that, knotting by means of it does not change the type of the simplest imbedding $\mathbf RP^2\to\mathbf R^4$. Figures: 6. Bibliography: 10 titles. 
@article{SM_1973_19_2_a1,
     author = {O. Ya. Viro},
     title = {Local knotting of submanifolds},
     journal = {Sbornik. Mathematics},
     pages = {166--176},
     year = {1973},
     volume = {19},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_19_2_a1/}
}
TY  - JOUR
AU  - O. Ya. Viro
TI  - Local knotting of submanifolds
JO  - Sbornik. Mathematics
PY  - 1973
SP  - 166
EP  - 176
VL  - 19
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1973_19_2_a1/
LA  - en
ID  - SM_1973_19_2_a1
ER  - 
%0 Journal Article
%A O. Ya. Viro
%T Local knotting of submanifolds
%J Sbornik. Mathematics
%D 1973
%P 166-176
%V 19
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1973_19_2_a1/
%G en
%F SM_1973_19_2_a1
O. Ya. Viro. Local knotting of submanifolds. Sbornik. Mathematics, Tome 19 (1973) no. 2, pp. 166-176. http://geodesic.mathdoc.fr/item/SM_1973_19_2_a1/

[1] Dzh. Milnor, Osobye tochki kompleksnykh giperpoverkhnostei, izd-vo «Mir», Moskva, 1971 | MR

[2] V. A. Rokhlin, “Dvumernye podmnogoobraziya chetyrekhmernykh mnogoobrazii”, Funkts. analiz, 5:1 (1971), 48–60 | MR | Zbl

[3] A. B. Sosinskii, “Razlozhenie uzlov”, Matem. sb., 81 (123) (1970), 145–158 | MR | Zbl

[4] R. H. Fox, “Covering spaces with singularities”, Lefschetz symposium, Princeton Math. Ser., 12, 1957, 243–257 | MR | Zbl

[5] R. H. Fox, “Some problems in knot theory”, Topology of 3-manifolds and related topics (Proc. the Univ. of Georgia Institute, 1961), Prentice Hall, Engelwood cliffs, New York, 1962, 168–176 | MR

[6] C. H. Giffen, “The generalized Smith conjecture”, Amer. J. Math., 88:1 (1966), 187–198 | DOI | MR | Zbl

[7] P. Orlik, “Weighted homogeneous polynomials and fundamental groups”, Topology, 9 (1970), 267–273 | DOI | MR | Zbl

[8] P. Orlik, “Smooth homotopy lens space”, Mich. Math. J., 16:3 (1969), 245–255 | DOI | MR | Zbl

[9] R. Palais, “Extending diffeomorphisms”, Proc. Amer. Math. Soc., 11 (1960), 274–277 | DOI | MR | Zbl

[10] E. C. Zeeman, “Twisting spun knots”, Trans. Amer. Math. Soc., 115 (1965), 471–495 | DOI | MR | Zbl