Geometry & Topology
- Geom. Topol.
- Volume 20, Number 3 (2016), 1773-1806.
Quotient singularities, eta invariants, and self-dual metrics
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.
Geom. Topol., Volume 20, Number 3 (2016), 1773-1806.
Received: 11 May 2015
Accepted: 21 August 2015
First available in Project Euclid: 16 November 2017
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Lock, Michael; Viaclovsky, Jeff. Quotient singularities, eta invariants, and self-dual metrics. Geom. Topol. 20 (2016), no. 3, 1773--1806. doi:10.2140/gt.2016.20.1773. https://projecteuclid.org/euclid.gt/1510859003