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

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.