Recent Results on the Size of Critical Sets

  • Dorin Andrica
  • Cornel Pintea


In the first part of this survey we review some special cases of \({\varphi }_{\mathcal{F}}\)-category of a pair (M, N) of manifolds such as φ-category, Morse-Smale characteristic, and Morse-Smale characteristic for circular functions. Section 2 presents examples of pairs with finite φ, and Sect. 3 provides lower estimates for the size of the critical sets in terms of topological dimension. We employ the cardinality when the manifolds admit maps with finitely many critical points and the topological dimension when no such maps exist.


Fundamental Group Boundary Component Hyperbolic Surface Critical Orbit Zero Codimension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The first author would like to express all his thanks to Professor Themistocles M. Rassias for the strong encouraging to prepare this survey.

The first author is partially supported by the King Saud University D.S.F.P. Program


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.College of ScienceKing Saud UniversityRiyadhSaudi Arabia
  2. 2.Department of Mathematics and Computer ScienceBabeş-Bolyai UniversityCluj-NapocaRomania

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