Continuous mappings with an infinite number of topologically critical points

• Autorzy: Cornel Pintea
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

topologically critical points; covering mappings; G-manifolds

Kategorie tematyczne

• 57R70: Critical points and critical submanifolds
• 57T20: Homotopy groups of topological groups and homogeneous spaces
• 57S15: Compact Lie groups of differentiable transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1997
• Tom: 67
• Numer: 1
• Strony: 87-93

Daty

wydano

1997

otrzymano

1996-03-20

poprawiono

1996-07-26

Twórcy

autor

Cornel Pintea

• Faculty of Mathematics, "Babeş-Bolyai" University, Str. Kogălniceanu 1, 3400 Cluj-Napoca, Romania

Bibliografia

• [1] D. Andrica and C. Pintea, Critical points of vector-valued functions, in: Proceedings of the 24th National Conference on Geometry and Topology, Timişoara 1993.
• [2] D. Rozpłoch-Nowakowska, Equivariant maps of joins of finite G-sets and an application to critical point theory, Ann. Polon. Math. 56 (1992) 195-211.
• [3] K. Kawakubo, The Theory of Transformation Groups, Oxford University Press, Oxford, 1991.
• [4] W. S. Massey, Algebraic Topology: An Introduction, Harcourt, Brace & World, New York, 1967.
• [5] R. S. Palais and C. L. Terng, Critical Point Theory and Submanifold Geometry, Lecture Notes in Math. 1353, Springer, 1988.
• [6] 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.