Estimating the rational LS-category of elliptic spaces

Abstract

An elliptic space is one whose rational homotopy and rational cohomol- ogy are both flnite dimensional. We prove, for Toomer's invariant, two improvements of the estimate of the Mapping theorem relying on data from the homotopy Lie al- gebra of the space. In particular, we show that if S is elliptic, cat0S ‚ dim L even + dim ZL odd ; where LS is the rational homotopy Lie algebra of S and ZLS its centre. Several interesting examples are presented to illustrate our results.