Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

$ 2$-sided embeddings of projective planes into $ 3$-manifolds


Author: Mitsuyuki Ochiai
Journal: Trans. Amer. Math. Soc. 274 (1982), 641-650
MSC: Primary 57N10; Secondary 57M40, 57Q25
MathSciNet review: 675072
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57N10, 57M40, 57Q25

Retrieve articles in all journals with MSC: 57N10, 57M40, 57Q25


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0675072-3
PII: S 0002-9947(1982)0675072-3
Article copyright: © Copyright 1982 American Mathematical Society