The linking pairings of orientable Seifert manifolds

Abstract

We compute the $p$-primary components of the linking pairings of orientable 3-manifolds admitting a fixed-point free $S^1$-action. Using this, we show that any non-singular linking pairing on a finite abelian group with homogeneous 2-primary summand is realized by such a manifold. However, some pairings on inhomogeneous 2-groups are not realizable by any Seifert fibred 3-manifold.

The paper has been rewritten to display the results more clearly, and errors flowing from an inconsistent choice of signs have been corrected. The formulation of the final result on 2-torsion has also been improved

Cited by in corpus (2)

• Complements of connected hypersurfaces in $S^4$
• Homology cobordism and Seifert fibered 3-manifolds