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

Published electronically:
May 2, 2000

MathSciNet review:
1670419

Full-text PDF Free Access

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 and S. Husseini,*A note on the category of the free loop space*, Proc. Amer. Math. Soc.**107**(1989), no. 2, 527–536. MR**984789**, 10.1090/S0002-9939-1989-0984789-4**[Go]**Claude Godbillon,*Éléments de topologie algébrique*, Hermann, Paris, 1971 (French). MR**0301725****[GoGo]**J. C. Gómez-Larrañaga and F. González-Acuña,*Lusternik-Schnirel′mann category of 3-manifolds*, Topology**31**(1992), no. 4, 791–800. MR**1191380**, 10.1016/0040-9383(92)90009-7**[Pi1]**Cornel Pintea,*A measure of non-immersability of the Grassmann manifolds in some Euclidean spaces*, Proc. Edinburgh Math. Soc. (2)**41**(1998), no. 1, 197–205. MR**1604325**, 10.1017/S0013091500019507**[Pi2]**Cornel Pintea,*Continuous mappings with an infinite number of topologically critical points*, Ann. Polon. Math.**67**(1997), no. 1, 87–93. MR**1455429****[Ta]**Floris Takens,*The minimal number of critical points of a function on a compact manifold and the Lusternik-Schnirelman category*, Invent. Math.**6**(1968), 197–244. MR**0236942**

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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:
http://dx.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