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

 

Involutions on Klein spaces $ M(p,\,q)$


Author: Paik Kee Kim
Journal: Trans. Amer. Math. Soc. 268 (1981), 377-409
MSC: Primary 57N10; Secondary 57S25
MathSciNet review: 632535
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Abstract: The Klein spaces $ M(p,\,q)$ are defined (up to homeomorphisms) to be the class of closed, orientable, irreducible $ 3$-manifolds with finite fundamental groups, in which a Klein bottle can be embedded. Their fundamental groups act freely on the $ 3$-sphere $ {S^3}$ in the natural way. We obtain a complete classification of the PL involutions on Klein spaces $ M(p,\,q)$. It can be applied to the study of some transformation group actions on $ {S^3}$ and double branched coverings of $ {S^3}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0632535-3
PII: S 0002-9947(1981)0632535-3
Keywords: $ 3$-manifolds, involutions
Article copyright: © Copyright 1981 American Mathematical Society