$2$-sided embeddings of projective planes into $3$-manifolds
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- by Mitsuyuki Ochiai PDF
- Trans. Amer. Math. Soc. 274 (1982), 641-650 Request permission
Abstract:
Let $M$ be a nonorientable closed $3$-manifold which admits a $2$-sided embedding of a projective plane. Then we first prove the following theorem: If $M$ has a Heegaard splitting of genus two, then $M$ is homeomorphic to ${P^{2}}\times {S^{1}}$. Next, let $M$ be a nonorientable $3$-manifold whose fundamental group is abelian. We verify that if $M$ has a Heegaard splitting of genus two, then $M$ is either the nonorientable $2$-sphere bundle over the circle or ${P^{2}}\times {S^{1}}$.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 274 (1982), 641-650
- MSC: Primary 57N10; Secondary 57M40, 57Q25
- DOI: https://doi.org/10.1090/S0002-9947-1982-0675072-3
- MathSciNet review: 675072