P2-irreducible manifold

In mathematics, a P2-irreducible manifold is a 3-manifold that is irreducible and contains no 2-sided R P 2 {\displaystyle \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.


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