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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Some $ 3$-manifolds which admit Klein bottles


Author: Paik Kee Kim
Journal: Trans. Amer. Math. Soc. 244 (1978), 299-312
MSC: Primary 57N10
MathSciNet review: 506621
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Abstract: Consider a closed, orientable, irreducible 3-manifold M with $ \left\vert {{\pi _1}(M)} \right\vert < \infty $, in which a Klein bottle can be embedded. We present a classification of the spaces M and show that, if $ {\pi _1}(M)$ is cyclic, then M is homeomorphic to a lens space. Note that all surfaces of even genus can be embedded in each space M. We also classify all free involutions on lens spaces whose orbit spaces contain Klein bottles.


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DOI: https://doi.org/10.1090/S0002-9947-1978-0506621-2
Keywords: 3-manifolds, lens spaces, involutions
Article copyright: © Copyright 1978 American Mathematical Society