The cohomology algebras of orientable Seifert manifolds and applications to Lusternik-Schnirelmann category

Abstract

This note gives a complete description of the cohomology algebra of any orientable Seifert manifold with Z/p coefficients, for an arbitrary prime p. As an application, the existence of a degree one map from an orientable Seifert manifold onto a lens space is completely determined. A second application shows that the Lusternik–Schnirelmann category for a large class of Seifert manifolds is equal to 3, which in turn is used to verify the Ganea conjecture for these Seifert manifolds.