Testing 3-manifolds for projective planes
WOLFGANG H. HEIL · Pacific Journal of Mathematics · 1973
It is well known that a closed 3-manifold M contains a (piecewise linearly embedded) essential separating 2-sphere if and only if π^M) is a nontrivial free product.In this paper necessary and sufficient conditions, in terms of πi(ilf), are given for the existence of a projective plane in M. If M is irreducible this condition is that πi(M) be an extension of Z or a nontrivial free product by Z%.In particular this provides a criterion for deciding which irreducible closed 3-manifolds are not PMrreducible.