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The Ganea and Whitehead Variants of the Lusternik–Schnirelmann Category

Published online by Cambridge University Press:  20 November 2018

Jean-Paul Doeraene  and
Mohammed El Haouari
Jean-Paul Doeraene
Affiliation:
Département de Mathématiques Pures et Appliquées, Université des Sciences et Technologies de Lille, 59655 Villeneuve D’Ascq Cedex, France e-mail: doeraene@math.univ-lille1.fr e-mail: haouari@agat.univ.lille1.fr
Mohammed El Haouari
Affiliation:
Département de Mathématiques Pures et Appliquées, Université des Sciences et Technologies de Lille, 59655 Villeneuve D’Ascq Cedex, France e-mail: doeraene@math.univ-lille1.fr e-mail: haouari@agat.univ.lille1.fr
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Abstract

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The Lusternik–Schnirelmann category has been described in different ways. Two major ones, the first by Ganea, the second by Whitehead, are presented here with a number of variants. The equivalence of these variants relies on the axioms of Quillen's model category, but also sometimes on an additional axiom, the so-called “cube axiom”.

Keywords

55P30Eckmann-Hilton duality
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 1 , 01 March 2006 , pp. 41 - 54
Copyright
Copyright © Canadian Mathematical Society 2006

References

[1] Baues, H., Algebraic homotopy. Cambridge Studies in Advanced mathematics 15, Cambridge University Press, Cambridge, 1989.Google Scholar
[2] Doeraene, J.-P., L.S.-category in a model category. J. Pure Appl. Algebra, 84(1993), no. 3, 215–261.Google Scholar
[3] Doeraene, J.-P., Homotopy pull backs, homotopy push outs and joins. Bull. Belg. Math. Soc. 5(1998), no. 1, 15–37.Google Scholar
[4] Ganea, T.., Lusternik-Schnirelmann category and strong category. Illinois J. Math 11(1967), 417–427.Google Scholar
[5] Hess, K. and Lemaire, J.-M., Generalizing a definition of Lusternik and Schnirelmann to model categories. J. Pure and Applied Algebra 91(1994), no. 1–3, 165–182.Google Scholar
[6] James, I. M., Reduced product spaces. Ann. of Math. 62(1955), 170–197.Google Scholar
[7] Mather, M., Pull-backs in homotopy theory. Canad. J. Math. 28(1976), no. 2, 225–263.Google Scholar
[8] Strøm, A., The homotopy category is a homotopy category. Arch. Math. 23(1972), 435–441.Google Scholar
[9] Sugawara, M., On a condition that a space is an H-space. Math. J. Okayama Univ. 6(1957), 109–129.Google Scholar
[10] Whitehead, G., The homology suspension. In: Colloque de topologie algébrique de Louvain, 1956, Georges Thone, Lige, 1957, pp. 89–95.Google Scholar