Un exemple où M cat f\(\neq A\,cat\,f\). (An example where M cat f\(\neq A\,cat\,f)\). (French) Zbl 0698.55008

Idrissi, Elhassan

C. R. Acad. Sci., Paris, Sér. I 310, No. 7, 599-602 (1990).

In a recent paper, K. Hess proved Ganea’s conjecture cat \(X\times S^ n=cat X+1\) for 1-connected rational spaces of finite type. Her proof is based on the fact that two invariants M cat X and A cat X related to the Lusternik-Schnirelmann category of a space are in fact equal. In this paper, the author gives an example to show that this result cannot be extended to the category of a map.

Reviewer: Y.Felix

MSC:

55P62	Rational homotopy theory
55M30	Lyusternik-Shnirel’man category of a space, topological complexity à la Farber, topological robotics (topological aspects)
13N05	Modules of differentials

Keywords:

rational spaces; Lusternik-Schnirelmann category