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 $(\Lambda V,d)$ and let $k\ge 2$ the biggest integer such that $d=\sum _{i\ge k}{d}_i$ with $d_i(V)\subseteq {\Lambda }^{i}V$. In \cite{murillo02} the authors showed that if $(\Lambda V,d_k)$ is morever elliptic then $cat(\Lambda V,d)=(k-2)dim{V}^{even}+dim{V}^{odd}.$ Our work focuses on the estimation of L.S.-category of such spaces in the case when $k=3$ and when $(\Lambda V,d_3)$ is not necessarily elliptic.