No abstract

Abstract. We show that the Lusternik-Schnirelmann category of the symplectic group Sp(3) is 5. This L-S category coincides with the cone length and the stable weak category.

We construct an explicit semifree model for the fiber join of two fibrations pW E ! B and p 0 W E 0 ! B from semifree models of p and p 0 . Using this model, we introduce a lower bound of the sectional category of a fibration p which can be calculated from any Sullivan model of p and which is closer to the sectional category of p than the classical cohomological lower bound given by the nilpotency of the kernel of p W H .BI ‫/ޑ‬ ! H .EI ‫./ޑ‬ In the special case of the evaluation fibration X I ! X X we obtain a computable lower bound of Farber's topological complexity TC.X /. We show that the difference between this lower bound and the classical cohomological lower bound can be arbitrarily large.55M30; 55P62

No abstract

No abstract