The size of some critical sets by means of dimension and algebraic \(\varphi\)-category. (English) Zbl 1255.58015

Pintea, Cornel

Topol. Methods Nonlinear Anal. 35, No. 2, 395-407 (2010).

The author investigates the size of some critical sets of a \(C^1\) function \(f:M\rightarrow N\), where \(M^n\) and \(N^n\) with \(n\geq 2\) are two compact connected manifolds. Roughly speaking, among the others results, he proves that if \(f\) is a mapping acting between manifolds with infinite algebraic \(\varphi-\)category of their fundamental groups, then \(f\) has zero degree and, consequently, high dimensional critical sets.

Reviewer: Pasquale Candito (Reggio Calabria)

MSC:

58K05	Critical points of functions and mappings on manifolds
57R70	Critical points and critical submanifolds in differential topology

Keywords:

critical point; degree of maps; algebraic \(\varphi\)-category