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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

$ 3$-manifolds which contain nonparallel projective planes


Author: Tsuyoshi Kobayashi
Journal: Proc. Amer. Math. Soc. 91 (1984), 314-318
MSC: Primary 57N10; Secondary 57Q65
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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0740193-0
PII: S 0002-9939(1984)0740193-0
Keywords: Heegaard splittings, nonparallel projective planes in $ 3$-manifolds
Article copyright: © Copyright 1984 American Mathematical Society