Continuous mappings with an infinite number of topologically critical points

Cornel Pintea

Annales Polonici Mathematici (1997)

  • Volume: 67, Issue: 1, page 87-93
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Cornel Pintea. "Continuous mappings with an infinite number of topologically critical points." Annales Polonici Mathematici 67.1 (1997): 87-93. <http://eudml.org/doc/270683>.

@article{CornelPintea1997,
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.},
author = {Cornel Pintea},
journal = {Annales Polonici Mathematici},
keywords = {topologically critical points; covering mappings; G-manifolds; topologically critical point; -manifolds; -category},
language = {eng},
number = {1},
pages = {87-93},
title = {Continuous mappings with an infinite number of topologically critical points},
url = {http://eudml.org/doc/270683},
volume = {67},
year = {1997},
}

TY - JOUR
AU - Cornel Pintea
TI - Continuous mappings with an infinite number of topologically critical points
JO - Annales Polonici Mathematici
PY - 1997
VL - 67
IS - 1
SP - 87
EP - 93
AB - 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.
LA - eng
KW - topologically critical points; covering mappings; G-manifolds; topologically critical point; -manifolds; -category
UR - http://eudml.org/doc/270683
ER -

References

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  1. [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. Zbl0870.57047
  2. [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. [3] K. Kawakubo, The Theory of Transformation Groups, Oxford University Press, Oxford, 1991. Zbl0744.57001
  4. [4] W. S. Massey, Algebraic Topology: An Introduction, Harcourt, Brace & World, New York, 1967. 
  5. [5] R. S. Palais and C. L. Terng, Critical Point Theory and Submanifold Geometry, Lecture Notes in Math. 1353, Springer, 1988. Zbl0658.49001
  6. [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. Zbl0198.56603

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