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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On $ 3$-manifolds that have finite fundamental group and contain Klein bottles


Author: J. H. Rubinstein
Journal: Trans. Amer. Math. Soc. 251 (1979), 129-137
MSC: Primary 57N10
MathSciNet review: 531972
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Abstract: The closed irreducible 3-manifolds with finite fundamental group and containing an embedded Klein bottle can be identified with certain Seifert fibre spaces. We calculate the isotopy classes of homeomorphisms of such 3-manifolds. Also we prove that a free involution acting on a manifold of this type, gives as quotient either a lens space or a manifold in this class. As a corollary it follows that a free action of $ {Z_8}$ or a generalized quaternionic group on $ {S^3}$ is equivalent to an orthogonal action.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0531972-6
PII: S 0002-9947(1979)0531972-6
Keywords: Seifert fibre space, isotopy class of homeomorphisms, free group action
Article copyright: © Copyright 1979 American Mathematical Society