| Title:
|
Hypersurfaces in $\mathbb R^n$ and critical points in their external region (English) |
| Author:
|
Manchón, P. M. G. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
1-9 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\mathbb R^{n+1} - M^n$. (English) |
| Keyword:
|
hypersurface in $\mathbb R^n$ |
| Keyword:
|
nondegenerate critical point |
| Keyword:
|
noncompact Morse Theory |
| Keyword:
|
h-cobordism |
| Keyword:
|
Palais-Smale condition |
| MSC:
|
57R70 |
| MSC:
|
57R80 |
| idZBL:
|
Zbl 1017.57014 |
| idMR:
|
MR1885451 |
| . |
| Date available:
|
2009-09-24T10:48:18Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127696 |
| . |
| Reference:
|
[1] M. H. Freedman and F. S. Quinn: Topology of 4-Manifolds.Princeton Univ. Press, Princeton, NJ., 1990. MR 1201584 |
| Reference:
|
[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 1226257 |
| Reference:
|
[3] V. Guillemin and A. Pollack: Differential Topology.Prentice-Hall, Englewood Cliffs, NJ., 1974. MR 0348781 |
| Reference:
|
[4] M. W. Hirsch: Differential Topology.Springer-Verlag, Berlin, 1976. Zbl 0356.57001, MR 0448362 |
| Reference:
|
[5] J. Margalef and E. Outerelo: Differential Topology.North Holland, Amsterdam, 1992. MR 1173211 |
| Reference:
|
[6] P. M. G. Manchón: Ph. D. Thesis.(1996), Universidad Complutense de Madrid. |
| Reference:
|
[7] J. Milnor: Lectures on the $h$-cobordism Theorem.Princeton Univ. Press, Princeton, NJ., 1965. Zbl 0161.20302, MR 0190942 |
| Reference:
|
[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 0130696 |
| Reference:
|
[9] R. S. Palais: Lusternik-Schnirelman theory on Banach manifolds.Topology 5 (1966), 115–132. Zbl 0143.35203, MR 0259955, 10.1016/0040-9383(66)90013-9 |
| Reference:
|
[10] R. S. Palais and S. Smale: A generalized Morse theory.Bull. Amer. Math. Soc. 70 (1964), 165–172. MR 0158411, 10.1090/S0002-9904-1964-11062-4 |
| . |
