On the Browder--Levine--Novikov Embedding Theorems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology and set theory, Tome 247 (2004), pp. 280-290.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this survey, we apply the concepts of complement and neighborhood to embeddings of manifolds into Euclidean space (in a codimension of at least three). We describe how a combination of these concepts gives a reduction of the embeddability and isotopy problems to algebraic problems. We also present a modern exposition of the Browder–Levine theorem on the realization of normal systems.
@article{TM_2004_247_a20,
     author = {M. Cencelj and D. Repov\v{s} and A. B. Skopenkov},
     title = {On the {Browder--Levine--Novikov} {Embedding} {Theorems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {280--290},
     publisher = {mathdoc},
     volume = {247},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2004_247_a20/}
}
TY  - JOUR
AU  - M. Cencelj
AU  - D. Repovš
AU  - A. B. Skopenkov
TI  - On the Browder--Levine--Novikov Embedding Theorems
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2004
SP  - 280
EP  - 290
VL  - 247
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2004_247_a20/
LA  - ru
ID  - TM_2004_247_a20
ER  - 
%0 Journal Article
%A M. Cencelj
%A D. Repovš
%A A. B. Skopenkov
%T On the Browder--Levine--Novikov Embedding Theorems
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2004
%P 280-290
%V 247
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2004_247_a20/
%G ru
%F TM_2004_247_a20
M. Cencelj; D. Repovš; A. B. Skopenkov. On the Browder--Levine--Novikov Embedding Theorems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology and set theory, Tome 247 (2004), pp. 280-290. http://geodesic.mathdoc.fr/item/TM_2004_247_a20/

[1] Alexander J. W., “On the subdivision of 3-space by polyhedron”, Proc. Nat. Acad. Sci. USA., 10 (1924), 6–8 | DOI

[2] Alexander J. W., “An example of a simply connected surface bounding a region which is not simply connected”, Proc. Nat. Acad. Sci. USA., 10 (1924), 8–10 | DOI

[3] Akhmetiev P., Repovš D., Skopenkov A., “Embedding products of low-dimensional manifolds in $\mathbb{R}^m$”, Topol. and Appl., 113 (2001), 7–12 | DOI | MR | Zbl

[4] Barden D., “Simply connected five-manifolds”, Ann. Math. Ser. 2, 82 (1965), 365–385 | DOI | MR | Zbl

[5] Brown M., “A proof of the generalized Schoenflies theorem”, Bull. Amer. Math. Soc., 66 (1960), 74–76 | DOI | MR | Zbl

[6] Browder W., “Embedding smooth manifolds”, Mezhdunarodnyi kongress matematikov (Moskva, 1966), Mir, M., 1968, 712–719 | MR

[7] Gitler S., “Immersion and embedding of manifolds”, Proc. Symp. Pure Math., 22 (1971), 87–96 | MR | Zbl

[8] Gluck H., “The embedding of two-spheres in the four-sphere”, Trans. Amer. Math. Soc., 104:2 (1962), 308–333 | DOI | MR | Zbl

[9] Gompf R., Stipsicz A., 4-Manifolds and Kirby calculus, Amer. Math. Soc., Providence, RI, 1999 | MR | Zbl

[10] Habegger N., “Knots and links in codimension greater than 2”, Topology, 25 (1986), 253–260 | DOI | MR | Zbl

[11] Haefliger A., “Enlacements de sphères en co-dimension supérieure à 2”, Comment. Math. Helv., 41 (1966), 51–72 | DOI | MR | Zbl

[12] Haefliger A., “Knotted spheres and related geometric topic”, Mezhdunarodnyi kongress matematikov (Moskva, 1966), Mir, M., 1968, 437–445 | MR

[13] Hantzsche W., “Einlagerung von Mannigfaltigkeiten in euklidische Räume”, Math. Ztschr., 43:1 (1937), 38–58 | DOI | MR | Zbl

[14] Hirsch M. W., “Immersions of manifolds”, Trans. Amer. Math. Soc., 93 (1959), 242–276 | DOI | MR | Zbl

[15] Haefliger A., Poenaru V., “La classification des immersions combinatoires”, Publ. Math. IHES, 1964, no. 23, 75–91 | MR

[16] Hopf H., “Systeme symmetrischen Bilinearformen und euklidische Modelle der projectiven Räume”, Vierteljahr. Naturforsch. Ges. Zürich., 85 (1940), 165–178 | MR

[17] Levine J., “On differentiable embeddings of simply-connected manifolds”, Bull. Amer. Math. Soc., 69 (1963), 806–809 | DOI | MR | Zbl

[18] Levine J., “Unknotting spheres in codimension 2”, Topology, 4 (1965), 9–16 | DOI | MR | Zbl

[19] Lickorish W. B. R., Siebenmann L. C., “Regular neighborhoods and the stable range”, Trans. Amer. Math. Soc., 139 (1969), 207–230 | DOI | MR | Zbl

[20] Mandelbaum R., “Four-dimensional topology: An introduction”, Bull. Amer. Math. Soc., 2 (1980), 1–159 | DOI | MR | Zbl

[21] Mazur B., “On embeddings of spheres”, Bull. Amer. Math. Soc., 65 (1959), 91–94 | DOI | MR

[22] Morse M., “A reduction of the Schoenflies extension problem”, Bull. Amer. Math. Soc., 66 (1960), 113–117 | DOI | MR

[23] Novikov S. P., “Gomotopicheski ekvivalentnye gladkie mnogoobraziya”, Izv. AN SSSR. Ser. mat., 28 (1964), 365–474

[24] Papakyriakopoulos C. D., “On Dehn's lemma and the asphericity of knots”, Ann. Math. Ser. 2, 66 (1957), 1–26 | DOI | MR | Zbl

[25] Repovš D., Brodsky N., Skopenkov A. B., “A classification of 3-thickenings of 2-polyhedra”, Topol. and Appl., 94 (1999), 307–314 | DOI | MR | Zbl

[26] Repovsh D., Skopenkov A., “Novye rezultaty o vlozheniyakh poliedrov i mnogoobrazii v evklidovy prostranstva”, UMN, 54:6 (1999), 61–109 | MR

[27] Rourke C. P., Sanderson B. J., Introduction to piecewise-linear topology, Ergebn. Math., 69, Springer, Berlin, 1972 ; Rurk K., Sanderson B., Vvedenie v kusochno lineinuyu topologiyu, Mir, M., 1974 | MR | Zbl | MR

[28] Rushing T. B., Topological embeddings, Acad. Press, New York, 1973 | MR | Zbl

[29] Smale S., “Generalized Poincare's conjecture in dimensions greater than 4”, Ann. Math. Ser. 2, 74 (1961), 391–466 | DOI | MR

[30] Stallings J., “On topologically unknotted spheres”, Ann. Math. Ser. 2, 77 (1963), 490–503 | DOI | MR | Zbl

[31] Steenrod N. E., Epstein D. B. A., Cohomology operations, Princeton Univ. Press, Princeton, 1962 ; Stinrod N., Epstein D., Kogomologicheskie operatsii, Nauka, M., 1983 | MR | Zbl | MR

[32] Thom R., “Une théorie intrinsèque des puissances de Steenrod”, Colloq. Topol. (Strasbourg, 1951), no. 6, La Bibliotheque Nationale et Universitaire de Strasbourg, 1952 | MR

[33] Wall C. T. C., “Classification problems in differential topology. IV: Thickenings”, Topology, 5 (1966), 73–94 | DOI | MR | Zbl

[34] Wall C. T. C., Surgery on compact manifolds, Acad. Press, London, 1970 | MR