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

Rubinstein, J. H.

doi:10.1090/S0002-9947-1979-0531972-6

On $3$-manifolds that have finite fundamental group and contain Klein bottles
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by J. H. Rubinstein

Trans. Amer. Math. Soc. 251 (1979), 129-137

DOI: https://doi.org/10.1090/S0002-9947-1979-0531972-6

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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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