Geodesic
Hypersurfaces in $\mathbb R^n$ and critical points in their external region
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 1, pp. 1-9 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper we study the hypersurfaces $M^n$ given as connected compact regular fibers of a differentiable map $f: \mathbb R^{n+1} \rightarrow \mathbb R$, in the cases in which $f$ has finitely many nondegenerate critical points in the unbounded component of $\mathbb R^{n+1} - M^n$.
In this paper we study the hypersurfaces $M^n$ given as connected compact regular fibers of a differentiable map $f: \mathbb R^{n+1} \rightarrow \mathbb R$, in the cases in which $f$ has finitely many nondegenerate critical points in the unbounded component of $\mathbb R^{n+1} - M^n$.
Classification : 57R70, 57R80
Keywords: hypersurface in $\mathbb R^n$; nondegenerate critical point; noncompact Morse Theory; h-cobordism; Palais-Smale condition 
@article{CMJ_2002_52_1_a0,
     author = {Manch\'on, P. M. G.},
     title = {Hypersurfaces in $\mathbb R^n$ and critical points in their external region},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1--9},
     year = {2002},
     volume = {52},
     number = {1},
     mrnumber = {1885451},
     zbl = {1017.57014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2002_52_1_a0/}
}
TY  - JOUR
AU  - Manchón, P. M. G.
TI  - Hypersurfaces in $\mathbb R^n$ and critical points in their external region
JO  - Czechoslovak Mathematical Journal
PY  - 2002
SP  - 1
EP  - 9
VL  - 52
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CMJ_2002_52_1_a0/
LA  - en
ID  - CMJ_2002_52_1_a0
ER  - 
%0 Journal Article
%A Manchón, P. M. G.
%T Hypersurfaces in $\mathbb R^n$ and critical points in their external region
%J Czechoslovak Mathematical Journal
%D 2002
%P 1-9
%V 52
%N 1
%U http://geodesic.mathdoc.fr/item/CMJ_2002_52_1_a0/
%G en
%F CMJ_2002_52_1_a0
Manchón, P. M. G. Hypersurfaces in $\mathbb R^n$ and critical points in their external region. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 1, pp. 1-9. http://geodesic.mathdoc.fr/item/CMJ_2002_52_1_a0/

[1] M. H. Freedman and F. S. Quinn: Topology of 4-Manifolds. Princeton Univ. Press, Princeton, NJ., 1990. | MR

[2] J. M.  Gamboa and C.  Ueno: Proper poynomial maps: the real case. Lectures Notes in Mathematics, 1524. Real Algebraic Geometry. Proceedings, Rennes, 1991, pp. 240–256. | MR

[3] V. Guillemin and A. Pollack: Differential Topology. Prentice-Hall, Englewood Cliffs, NJ., 1974. | MR

[4] M. W.  Hirsch: Differential Topology. Springer-Verlag, Berlin, 1976. | MR | Zbl

[5] J. Margalef and E. Outerelo: Differential Topology. North Holland, Amsterdam, 1992. | MR

[6] P. M. G. Manchón: Ph. D. Thesis. (1996), Universidad Complutense de Madrid.

[7] J. Milnor: Lectures on the $h$-cobordism Theorem. Princeton Univ. Press, Princeton, NJ., 1965. | MR | Zbl

[8] J. Milnor: A procedure for killing the homotopy groups of differentiable manifolds. Proc. Sympos. Pure Math, Vol. 3 Amer. Math. Soc. Providence, R.I, 1961, pp. 39–55. | MR

[9] R. S. Palais: Lusternik-Schnirelman theory on Banach manifolds. Topology 5 (1966), 115–132. | DOI | MR | Zbl

[10] R. S. Palais and S. Smale: A generalized Morse theory. Bull. Amer. Math. Soc. 70 (1964), 165–172. | DOI | MR