2004/03/23 by Martin Arkowitz, Arkowitz, Martin, Jeffrey Strom +1 · 2 citations
Computer Science · Mathematics · #Constraint Satisfaction and Optimization #Data Management and Algorithms #math.AT #msc:55M30 #msc:55P99
paper · pdf · doi:10.48550/arxiv.math/0403387
18 pages
arxiv created 2004/03/23 · arxiv updated 2009/12/01
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.