ArticleOriginal scientific text
Title
Continuous mappings with an infinite number of topologically critical points
Authors 1
Affiliations
- Faculty of Mathematics, "Babeş-Bolyai" University, Str. Kogălniceanu 1, 3400 Cluj-Napoca, Romania
Abstract
We prove that the topological φ-category of a pair (M,N) of topological manifolds is infinite if the algebraic φ-category of the pair of fundamental groups (π₁(M),π₁(N)) is infinite. Some immediate consequences of this fact are also pointed out.
Keywords
topologically critical points, covering mappings, G-manifolds
Bibliography
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- R. S. Palais and C. L. Terng, Critical Point Theory and Submanifold Geometry, Lecture Notes in Math. 1353, Springer, 1988.
- F. Takens, The minimal number of critical points of a function on a compact manifold and the Lusternik-Schnirelmann category, Invent. Math. 6 (1968), 197-244.
Pages:
87-93
Main language of publication
English
Received
1996-03-20
Accepted
1996-07-26
Published
1997
Exact and natural sciences