On L.S.-category of a family of rational elliptic spaces

Abstract

Let X be a finite type simply connected rationally elliptic CW-complex with Sullivan minimal model $(ΛV, d)$ and let $k \geq 2$ the biggest integer such that $d=\sum \limits_{\underset{}{i\geq k}}d_i$ with $d_i(V) \subseteq Λ^iV$. In \cite{murillo02} the authors showed that if $(ΛV,d_k)$ is morever elliptic then $cat(ΛV,d)=(k-2)dimV^{even} + dimV^{odd}.$ Our work focuses on the estimation of L.S.-category of such spaces in the case when $k=3$ and when $(ΛV,d_3)$ is not necessarily elliptic.