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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
DOI: https://doi.org/10.1090/S0002-9947-1981-0632535-3
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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Keywords: <IMG WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$3$">-manifolds, involutions
Article copyright: © Copyright 1981 American Mathematical Society