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The sectional category of a map | | Martin Arkowitz
; Jeffrey Strom
; | | Date: |
23 Mar 2004 | | Subject: | Algebraic Topology MSC-class: 55M30 (primary), 55P99 (secondary) | math.AT | | Affiliation: | Dartmouth College), Jeffrey Strom (Western Michigan University | | Abstract: | We study a generalization of the Svarc genus of a fiber map. For an arbitrary collection E of spaces and a map f:X-->Y, we define a numerical invariant, the E-sectional category of f, in terms of open covers of Y. We obtain several basic features of E-sectional category, including those dealing with homotopy domination and homotopy pushouts. We then give three simple properties which characterize the E-sectional category. In the final section we obtain inequalities for the E-sectional category of a composition and inequalities relating the E-sectional category to the Fadell-Husseini category of a map and the Clapp-Puppe category of a map. | | Source: | arXiv, math.AT/0403387 | | Services: | Forum | Review | PDF | Favorites | |
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