Abstract
Kawauchi and Kojima have shown that for any linking pairing (G, φ) on a finite abelian group G there is a closed, connected, oriented 3-manifold, M ,w ithH1(M )= G and linking form λM ∼ φ. Our object is to refine this theorem by proving that any linking pairing on a finite abelian group can be realized as the linking form of an oriented Seifert manifold which is a rational homology sphere. In particular, since such Seifert manifolds are irreducible, any linking pairing on a finite abelian group would then be isomorphic to the linking form of an irreducible 3-manifold. We refer to this as the linking form conjecture.
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