Volume 23, issue 2 (2019)

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

Volume 28
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

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 Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Gauge theory on Aloff–Wallach spaces

Gavin Ball and Goncalo Oliveira

Geometry & Topology 23 (2019) 685–743
Abstract

For gauge groups U(1) and SO(3) we classify invariant G2 –instantons for homogeneous coclosed G2 –structures on Aloff–Wallach spaces Xk,l. As a consequence, we give examples where G2 –instantons can be used to distinguish between different strictly nearly parallel G2 –structures on the same Aloff–Wallach space. In addition to this, we find that while certain G2 –instantons exist for the strictly nearly parallel G2 –structure on X1,1, no such G2 –instantons exist for the 3–Sasakian one. As a further consequence of the classification, we produce examples of some other interesting phenomena, such as irreducible G2 –instantons that, as the structure varies, merge into the same reducible and obstructed one and G2 –instantons on nearly parallel G2 –manifolds that are not locally energy-minimizing.

Keywords
G2 geometry, gauge theory, instantons, Aloff–Wallach spaces, tri-Sasakian, nearly parallel, cocalibrated
Mathematical Subject Classification 2010
Primary: 53C07, 53C29, 53C38, 57R57
References
Publication
Received: 23 June 2017
Revised: 31 May 2018
Accepted: 18 September 2018
Published: 8 April 2019
Proposed: Simon Donaldson
Seconded: Tobias H Colding, Tomasz Mrowka
Authors
Gavin Ball
Department of Mathematics
Duke University
Durham, NC
United States
Goncalo Oliveira
Departamento de Matemàtica Aplicada, Instituto de Matemática e Estatística
Universidade Federal Fluminense
Niterói
Rio de Janeiro-RJ
Brazil