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Abstract: Based on a Whitehead-type characterization of the sectional category wedevelop the notion of weak sectional category. This is a new lower bound of thesectional category, which is inspired by the notion of weak category in thesense of Berstein-Hilton. We establish several properties and inequalities,including the fact that the weak sectional category is a better lower bound forthe sectional category than the classical one given by the nilpotency of thekernel of the induced map in cohomology. Finally, we apply our results in thestudy of the topological complexity in the sense of Farber.



Author: J.M.G. Calcines, L. Vandembroucq

Source: https://arxiv.org/



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