In
mathematics, a P
2-irreducible manifold is a
3-manifold that is
irreducible and contains no
2-sided
In mathematics, specifically in topology of manifolds, a compact codimension-one submanifold F of a manifold M is said to be 2-sided in M when there is an embedding
::h\colon F\times 1,1to M
with h(x,0)=x for each x\in F and
::h(F\times 1,1 ...
(
real projective plane
In mathematics, the real projective plane is an example of a compact non- orientable two-dimensional manifold; in other words, a one-sided surface. It cannot be embedded in standard three-dimensional space without intersecting itself. It has ...
). An
orientable manifold is P
2-irreducible if and only if it is irreducible.
[.] Every non-orientable P
2-irreducible manifold is a
Haken manifold.
[.]
References
3-manifolds
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