Revistes Catalanes amb Accés Obert (RACO)

LS-catégorie de CW-complexes à 3 cellules en théorie homotopique $R$-locale

H. Scheerer, D. Tanré


We study the Lusternik-Schnirelmann category of some CW-complexes with 3 cells, built on $Y=S^{2n}\cup_{k[\iota_{2n},\iota_{2n}]}e^{4n}$. In particular, we prove that an $R$-local space, in the sense of D. Anick, of LS-category 3 and of the homotopy type of a CW-complex with 3 $R$-cells, has a cup-product of length 3 in its algebra of cohomology. This result is no longer true in the framework of mild spaces.

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