The $\bar{\mu }$-invariant of Seifert fibered homology spheres and the Dirac operator

Abstract

We derive a formula for the $\bar{\mu }$-invariant of a Seifert fibered homology sphere in terms of the eta-invariant of its Dirac operator. As a consequence, we obtain a vanishing result for the index of certain Dirac operators on plumbed 4-manifolds bounding such spheres.

arXiv comment13 pages