The category of nilmanifolds (Q1198794)

The author uses the techniques of rational homotopy theory to prove that for a nilmanifold \(M\), we have: \(\dim M=\text{rank}(\pi_ 1(M))=\text{cat}(M)=e_ 0(M)\). Here \(e_ 0(M)\) is the invariant introduced by Toomer and defined as the largest integer \(p\) such that \(E^{p,*}_ \infty\neq 0\) in the Moore spectral sequence: \(\text{Tor}_{H^*(\Omega M;\mathbb{Q})}(\mathbb{Q},\mathbb{Q})\to H^*(M;\mathbb{Q})\).