On 3-manifolds that have finite fundamental group and contain Klein bottles
Open Access
- 1 January 1979
- journal article
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 251, 129-137
- https://doi.org/10.1090/s0002-9947-1979-0531972-6
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 {Z_8} or a generalized quaternionic group on S 3 {S^3} is equivalent to an orthogonal action.Keywords
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