Abstract
We study a generalization of the Svarc genus of a fibre map. For an arbitrary collection ɛ of spaces and a map f : X → Y, we define a numerical invariant, the ɛ-sectional category of f, in terms of open covers of Y. We obtain several basic properties of ɛ-sectional category, including those dealing with homotopy domination and homotopy pushouts. We then give three simple axioms which characterize the ɛ-sectional category. In the final section, we obtain inequalities for the ɛ-sectional category of a composition and inequalities relating the ɛ-sectional category to the Fadell–Husseini category of a map and the Clapp–Puppe category of a map.
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More From: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
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