A Linking Form Conjecture for 3-manifolds

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, with H1(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.

Keywords: Seifert manifolds, linking form