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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

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