P2-irreducible manifold

In mathematics, a P²-irreducible manifold is a 3-manifold that is irreducible and contains no 2-sided $ℝP^2$ (real projective plane). An orientable manifold is P²-irreducible if and only if it is irreducible. Every non-orientable P²-irreducible manifold is a Haken manifold.

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