A construction of certain 3-manifolds with orientation reversing involution
In the reviewer's paper ``On 3-manifolds admitting orientation-reversing involutions'' [ibid. 33, 571-589 (1981; Zbl 0474.57006)], it is observed that the first homology group of a closed orientable 3-manifold with an orientation reversing involution has the torsion part of a direct double or a direct sum of a direct double and the group of order two. Further, it is shown that any finitely generated Abelian group with torsion part a direct double is realizable by an irreducible one, but if the whole group is a direct sum of a direct double of odd order (\(\neq 1)\) and the group of order two, then it is not realizable by any irreducible one. In this paper, the author proves by a concrete construction that any finitely generated Abelian group except for this special case is realizable by an irreducible one if its torsion part is a direct double or a direct sum of a direct double and the group of order two.
3-manifolds admitting orientation-reversing involutions
scientific article; zbMATH DE number 4038828