S~2- and P~2-category of manifolds

摘要

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_1→M~n factor homotopically through maps W_i→ S~2 (resp. P~2). We characterize all closed n-manifolds of S~2-category 2 and the fundamental groups of all closed n-manifolds of P~2-category 2.