Recent Results on the Size of Critical Sets

Dorin Andrica () and Cornel Pintea ()
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Dorin Andrica: King Saud University, College of Science
Cornel Pintea: Babeş-Bolyai University, Department of Mathematics and Computer Science

A chapter in Essays in Mathematics and its Applications, 2012, pp 17-35 from Springer

Abstract: Abstract 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.

Keywords: Fundamental Group; Boundary Component; Hyperbolic Surface; Critical Orbit; Zero Codimension (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-28821-0_2

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DOI: 10.1007/978-3-642-28821-0_2

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