The size of some critical sets by means of dimension and algebraic $\varphi$-category
Keywords
Critical points/values, degree of maps, algebraic $\varphi$-categoryAbstract
Let $M^n$, $N^n$, $n\geq 2$, be compact connected manifolds. We first observe that mappings of zero degree have high dimensional critical sets and show that the only possible degree is zero for maps $f\colon M\to N$, under the assumption on the index $[\pi_1(N):{\rm Im}(f_*)]$ to be infinite. By contrast with the described situation one shows, after some estimates on the algebraic $\varphi$-category of some pairs of finite groups, that a critical set of smaller dimension keeps the degree away from zero.Downloads
Published
2010-04-23
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1.
PINTEA, Cornel. The size of some critical sets by means of dimension and algebraic $\varphi$-category. Topological Methods in Nonlinear Analysis. Online. 23 April 2010. Vol. 35, no. 2, pp. 395 - 407. [Accessed 10 November 2024].
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