The linking pairings of orientable Seifert manifolds

TL;DR

This paper computes the p-primary components of linking pairings in orientable Seifert manifolds with free S^1-actions, showing which pairings can be realized by such manifolds and identifying limitations.

Contribution

It provides a detailed computation of linking pairings in Seifert manifolds and characterizes which pairings are realizable by these manifolds.

Findings

Non-singular pairings with homogeneous 2-primary summands are realizable.

Some pairings on inhomogeneous 2-groups are not realizable.

The work advances understanding of the relationship between Seifert manifolds and their linking pairings.

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.