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2016 Quotient singularities, eta invariants, and self-dual metrics
Michael Lock, Jeff Viaclovsky
Geom. Topol. 20(3): 1773-1806 (2016). DOI: 10.2140/gt.2016.20.1773


There are three main components to this article:

  1. A formula for the η–invariant of the signature complex for any finite subgroup of SO(4) acting freely on S3 is given. An application of this is a nonexistence result for Ricci-flat ALE metrics on certain spaces.

  2. 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 SO(4) which act freely on S3. Some applications of this formula to the realm of self-dual and scalar-flat Kähler metrics are also discussed.

  3. Two infinite families of scalar-flat anti-self-dual ALE spaces with groups at infinity not contained in U(2) are constructed. Using these spaces, examples of self-dual metrics on n # 2 are obtained for n 3. These examples admit an S1–action, but are not of LeBrun type.


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Michael Lock. Jeff Viaclovsky. "Quotient singularities, eta invariants, and self-dual metrics." Geom. Topol. 20 (3) 1773 - 1806, 2016.


Received: 11 May 2015; Accepted: 21 August 2015; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1348.53054
MathSciNet: MR3523069
Digital Object Identifier: 10.2140/gt.2016.20.1773

Primary: 53C25, 58J20

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.20 • No. 3 • 2016
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