There are three main components to this article:
A formula for the –invariant of the signature complex for any finite subgroup of acting freely on is given. An application of this is a nonexistence result for Ricci-flat ALE metrics on certain spaces.
A formula for the orbifold correction term that arises in the index of the self-dual deformation complex is proved for all finite subgroups of which act freely on . Some applications of this formula to the realm of self-dual and scalar-flat Kähler metrics are also discussed.
Two infinite families of scalar-flat anti-self-dual ALE spaces with groups at infinity not contained in are constructed. Using these spaces, examples of self-dual metrics on are obtained for . These examples admit an –action, but are not of LeBrun type.
"Quotient singularities, eta invariants, and self-dual metrics." Geom. Topol. 20 (3) 1773 - 1806, 2016. https://doi.org/10.2140/gt.2016.20.1773