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Differentiable mappings with an infinite number of critical points
Author(s):
C.
Pintea
Journal:
Proc. Amer. Math. Soc.
128
(2000),
3435-3444.
MSC (2000):
Primary 55Q05, 57R70, 57S25
Posted:
May 2, 2000
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Abstract:
In this paper we shall give some sufficient conditions in order that the so-called  -category of a pair  of differentiable manifolds be infinite.
References:
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- [AnPi]
- D. Andrica, C. Pintea, Critical points of vector-valued functions, Proc. 24
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- R-N. Danuta, Equivariant maps of joins of finite G-sets and an application to critical point theory, Ann. Polonici Math. L VI.2(1992).
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- E. Fadell, S. Husseini, A note on the category of the free loop space, Proc. Amer. Math. Soc., 107(1989), 527-536. MR 90a:55008
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- C. Godbillon, Éléments de Topologie Algébrique, Collection Méthodes, Hermann Paris, 1971. MR 46:880
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- [Pi1]
- C. Pintea, A measure of non-immersability of the Grassmann manifolds in some Euclidean spaces, Proc. Edinburgh Math. Soc. 41(1998), 197-206. MR 98k:57051
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- C. Pintea, Continuous mappings with an infinite number of topologically critical points, Ann. Polonici Math., LXVII.1 (1997), 87-93. MR 98d:57059
- [Ta]
- F. Takens, The minimal number of critical points of a function on a compact manifold and the Lusternik-Schnirelmann Category, Invent. Math. 6, 197-244(1968). MR 38:5235
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Additional Information:
C.
Pintea
Affiliation:
Faculty of Mathematics, ``Babes-Bolyai" University, Str. M. Kogalniceanu 1, 3400 Cluj-Napoca, Romania
Email:
cpintea@math.ubbcluj.ro
DOI:
10.1090/S0002-9939-00-05392-2
PII:
S 0002-9939(00)05392-2
Keywords:
$G$-manifolds,
critical points,
critical orbits,
homotopy groups
Received by editor(s):
October 16, 1997
Received by editor(s) in revised form:
December 18, 1998
Posted:
May 2, 2000
Additional Notes:
This paper is a part of the author's doctoral dissertation.
Communicated by:
Ralph Cohen
Copyright of article:
Copyright
2000,
American Mathematical Society
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