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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
$\mathrm{G}_2$–instantons on generalised Kummer constructions

Thomas Walpuski

Geometry & Topology 17 (2013) 2345–2388
Abstract

In this article we introduce a method to construct G2–instantons on G2–manifolds arising from Joyce’s generalised Kummer construction. The method is based on gluing ASD instantons over ALE spaces to flat bundles on G2–orbifolds of the form T7Γ. We use this construction to produce non-trivial examples of G2–instantons.

Keywords
$\mathrm{G}_2$–manifolds, $\mathrm{G}_2$–instantons, gauge theory, gluing constructions
Mathematical Subject Classification 2010
Primary: 53C07
Secondary: 53C25, 53C38
References
Publication
Received: 26 January 2012
Revised: 17 December 2012
Accepted: 2 May 2013
Published: 22 August 2013
Proposed: Ronald Stern
Seconded: Richard Thomas, Simon Donaldson
Authors
Thomas Walpuski
Department of Mathematics
Imperial College London
180 Queen’s Gate
London SW7 2AZ
UK