P²-irreducible
Encyclopedia
In mathematics
, a 3-manifold
is P2-irreducible if it is irreducible and contains no 2-sided
(real projective plane
).
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a 3-manifold
3-manifold
In mathematics, a 3-manifold is a 3-dimensional manifold. The topological, piecewise-linear, and smooth categories are all equivalent in three dimensions, so little distinction is made in whether we are dealing with say, topological 3-manifolds, or smooth 3-manifolds.Phenomena in three dimensions...
is P2-irreducible if it is irreducible and contains no 2-sided
2-sided
In topology, a compact codimension one submanifold F of a manifold M is said to be 2-sided in M when there is an embeddingwith h=x for each x\in F andIn other words, if its normal bundle is trivial....
(real projective planeReal projective plane
In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold, that is, a one-sided surface. It cannot be embedded in our usual three-dimensional space without intersecting itself...
).