# Hypersurfaces in ${\mathbb{R}}^{n}$ and critical points in their external region

Czechoslovak Mathematical Journal (2002)

- Volume: 52, Issue: 1, page 1-9
- ISSN: 0011-4642

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topManchón, P. M. G.. "Hypersurfaces in $\mathbb {R}^n$ and critical points in their external region." Czechoslovak Mathematical Journal 52.1 (2002): 1-9. <http://eudml.org/doc/30679>.

@article{Manchón2002,

abstract = {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 $\mathbb \{R\}^\{n+1\} - M^n$.},

author = {Manchón, P. M. G.},

journal = {Czechoslovak Mathematical Journal},

keywords = {hypersurface in $\mathbb \{R\}^n$; nondegenerate critical point; noncompact Morse Theory; h-cobordism; Palais-Smale condition; nondegenerate critical point; noncompact Morse theory; -cobordism; Palais-Smale condition; hypersurface},

language = {eng},

number = {1},

pages = {1-9},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Hypersurfaces in $\mathbb \{R\}^n$ and critical points in their external region},

url = {http://eudml.org/doc/30679},

volume = {52},

year = {2002},

}

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

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 52

IS - 1

SP - 1

EP - 9

AB - 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 $\mathbb {R}^{n+1} - M^n$.

LA - eng

KW - hypersurface in $\mathbb {R}^n$; nondegenerate critical point; noncompact Morse Theory; h-cobordism; Palais-Smale condition; nondegenerate critical point; noncompact Morse theory; -cobordism; Palais-Smale condition; hypersurface

UR - http://eudml.org/doc/30679

ER -

## References

top- Topology of 4-Manifolds, Princeton Univ. Press, Princeton, NJ., 1990. (1990) MR1201584
- Proper poynomial maps: the real case, Lectures Notes in Mathematics, 1524. Real Algebraic Geometry. Proceedings, Rennes, 1991, pp. 240–256. (1991) MR1226257
- Differential Topology, Prentice-Hall, Englewood Cliffs, NJ., 1974. (1974) MR0348781
- Differential Topology, Springer-Verlag, Berlin, 1976. (1976) Zbl0356.57001MR0448362
- Differential Topology, North Holland, Amsterdam, 1992. (1992) MR1173211
- Ph. D. Thesis, (1996), Universidad Complutense de Madrid. (1996)
- Lectures on the $h$-cobordism Theorem, Princeton Univ. Press, Princeton, NJ., 1965. (1965) Zbl0161.20302MR0190942
- 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. (1961) MR0130696
- 10.1016/0040-9383(66)90013-9, Topology 5 (1966), 115–132. (1966) Zbl0143.35203MR0259955DOI10.1016/0040-9383(66)90013-9
- 10.1090/S0002-9904-1964-11062-4, Bull. Amer. Math. Soc. 70 (1964), 165–172. (1964) MR0158411DOI10.1090/S0002-9904-1964-11062-4

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