Differentiable mappings with an infinite number of critical points

Author:
C. Pintea

Journal:
Proc. Amer. Math. Soc. **128** (2000), 3435-3444

MSC (2000):
Primary 55Q05, 57R70, 57S25

DOI:
https://doi.org/10.1090/S0002-9939-00-05392-2

Published electronically:
May 2, 2000

MathSciNet review:
1670419

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Abstract | References | Similar Articles | Additional Information

In this paper we shall give some sufficient conditions in order that the so-called -category of a pair of differentiable manifolds be infinite.

**[AnPi]**D. Andrica, C. Pintea,*Critical points of vector-valued functions*, Proc. 24Conf. Geom. Top., Univ. Timisoara.**[Da]**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).**[FaHu]**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****[Go]**C. Godbillon,*Éléments de Topologie Algébrique*, Collection Méthodes, Hermann Paris, 1971. MR**46:880****[GoGo]**I.C. Gómez-Larañaga, F. Gonzales-Acuña,*Lusternik-Schnirelmann category of 3-manifolds*, Topology Vol. 31, No. 4, pp. 791-800, 1992. MR**93j:55005****[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****[Pi2]**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, “Babeş-Bolyai" University, Str. M. Kogălniceanu 1, 3400 Cluj-Napoca, Romania

Email:
cpintea@math.ubbcluj.ro

DOI:
https://doi.org/10.1090/S0002-9939-00-05392-2

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

Published electronically:
May 2, 2000

Additional Notes:
This paper is a part of the author’s doctoral dissertation.

Communicated by:
Ralph Cohen

Article copyright:
© Copyright 2000
American Mathematical Society