S2- and P2-category of manifolds

J. C. Gomez-Larranaga, F. Gonzalez-Acuna, W. Heil

A closed topological n-manifold M^n is of S^2- (resp. P^2)-category 2 if it can be covered by two open subsets W_1, W_2 such that the inclusions W_i \to M^n factor homotopically through maps W_i \to S^2 (resp., P^2). We characterize all closed n-manifold of S^2-category 2 and of P^2-category 2.