Volume 20, issue 3 (2016)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 26, 1 issue

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
Quotient singularities, eta invariants, and self-dual metrics

Michael T Lock and Jeff A Viaclovsky

Geometry & Topology 20 (2016) 1773–1806

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.
quotient singularities, eta invariants, self-dual, ALE, orbifold
Mathematical Subject Classification 2010
Primary: 53C25, 58J20
Received: 11 May 2015
Accepted: 21 August 2015
Published: 4 July 2016
Proposed: Simon Donaldson
Seconded: Tobias H Colding, Ciprian Manolescu
Michael T Lock
Department of Mathematics
University of Texas
Austin, TX 78712
United States
Jeff A Viaclovsky
Department of Mathematics
University of Wisconsin
Madison, WI 53706
United States