Geodesic
Suspension of the Lusternik-Schnirelmann Category
Canadian journal of mathematics, Tome 22 (1970) no. 6, pp. 1129-1132

Voir la notice de l'article provenant de la source Cambridge University Press

Let cat be the Lusternik-Schnirelmann category structure as defined by Whitehead [6] and let be the category structure as defined by Ganea [2],We prove that and It is known that w ∑ cat X = conil X for connected X. Dually, if X is simply connected, 1. We work in the category of based topological spaces with the based homotopy type of CW-complexes and based homotopy classes of maps. We do not distinguish between a map and its homotopy class. Constant maps are denoted by 0 and identity maps by 1.We recall some notions from Peterson's theory of structures [5; 1] which unify the definitions of the numerical homotopy invariants akin to the Lusternik-Schnirelmann category. 
Gilbert, William J. Suspension of the Lusternik-Schnirelmann Category. Canadian journal of mathematics, Tome 22 (1970) no. 6, pp. 1129-1132. doi: 10.4153/CJM-1970-131-6
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[1] 1. Berstein, I. and Hilton, P. J., Homomorphisms of homotopy structures, Topologie et géométrie différentielle, Séminaire C. Ehresmann, Vol. 5 (Institut H. Poincaré, Paris, 1963). Google Scholar

[2] 2. Ganea, T., A generalization of the homology and homotopy suspension, Comment. Math. Helv. 39 (1965), 295–322. Google Scholar

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[4] 4. Gilbert, W. J., Some examples for weak category and conilpotency, Illinois J. Math. 12 (1968), 421–432. Google Scholar

[5] 5. Peterson, F. P., Numerical invariants of homotopy type, pp. 79–83 in Colloquium on Algebraic Topology (Matematisk Institut, Aarhus Univ., Aarhus, 1962). Google Scholar

[6] 6. Whitehead, G. W., The homology suspension, pp. 89–95 in Colloque de topologie algébrique, Louvain, 1956 (Masson et Cie, Paris, 1957). Google Scholar

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