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The sectional category of a map

Published online by Cambridge University Press:  12 July 2007

M. Arkowitz
Affiliation:
Dartmouth College, Hanover, NH 03755, USA (martin.arkowitz@dartmouth.edu)
J. Strom
Affiliation:
Western Michigan University, Kalamazoo, MI 49008, USA (jeff.strom@wmich.edu)

Abstract

We study a generalization of the Svarc genus of a fibre map. For an arbitrary collection ɛ of spaces and a map f : XY, 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.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2004

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