Involutions on Klein spaces 𝑀(𝑝,𝑞)

Kim, Paik Kee

doi:10.1090/S0002-9947-1981-0632535-3

Involutions on Klein spaces $M(p, q)$
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by Paik Kee Kim

Trans. Amer. Math. Soc. 268 (1981), 377-409

DOI: https://doi.org/10.1090/S0002-9947-1981-0632535-3

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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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