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On the Mapping Theorem for Lusternik-Schnirelmann Category II

Published online by Cambridge University Press:  20 November 2018

Yves Félix  and
Jean-Michel Lemaire
Yves Félix
Affiliation:
Université Catholique de Louvain, Louvain, Belgique
Jean-Michel Lemaire
Affiliation:
Université de Nice, Nice, France
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Let X and Y be 1-connected spaces having the homotopy type of cw-complexes.

Definition 0.1. A continuous map f:X → Y is Ω-split if Ωf:ΩX → ΩY admits a retraction up to homotopy.

In [6] we prove the following “mapping theorem”:

THEOREM 0.1. (a) If f is Ω-split, then cat(X) ≦ cat(Y);

(b) If π*(f) is split injective and ΩY has the homotopy type of a product of Eilenberg-MacLane spaces, then f is Ω-split.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 6 , 01 December 1988 , pp. 1389 - 1398
Copyright
Copyright © Canadian Mathematical Society 1988

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