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$ 3$-manifolds which contain nonparallel projective planes


Author: Tsuyoshi Kobayashi
Journal: Proc. Amer. Math. Soc. 91 (1984), 314-318
MSC: Primary 57N10; Secondary 57Q65
DOI: https://doi.org/10.1090/S0002-9939-1984-0740193-0
MathSciNet review: 740193
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Abstract: We show that if a closed, connected $ 3$-manifold with a Heegaard splitting of genus three contains mutually disjoint and nonparallel $ 2$-sided projective planes, then the manifold is homeomorphic to the connected sum of $ {P^2} \times {S^1}$ and the twisted $ 2$-sphere bundle over the circle.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0740193-0
Keywords: Heegaard splittings, nonparallel projective planes in $ 3$-manifolds
Article copyright: © Copyright 1984 American Mathematical Society

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