P2-irreducible manifold

In mathematics, a P²-irreducible manifold is a 3-manifold that is irreducible and contains no 2-sided ${\mathbb R}P^{2}$ (real projective plane). An orientable manifold is P²-irreducible if and only if it is irreducible.^[1] Every non-orientable P²-irreducible manifold is a Haken manifold.^[2]

References

1. Hazewinkel, Michiel (2001), Encyclopaedia of Mathematics, Supplement III, Volume 13, Springer, p. 183, ISBN 9781556080104.
2. Rassias, George M.; Stratopoulos, George (1989), Geometry and Topology, World Scientific, p. 33, ISBN 9789971506780.