G2–instantons on generalised Kummer constructions

Walpuski, Thomas

doi:10.2140/gt.2013.17.2345

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$\mathrm{G}_2$–instantons on generalised Kummer constructions

Thomas Walpuski

Geometry & Topology 17 (2013) 2345–2388

DOI: 10.2140/gt.2013.17.2345

Abstract

In this article we introduce a method to construct $G_{2}$ –instantons on $G_{2}$ –manifolds arising from Joyce’s generalised Kummer construction. The method is based on gluing ASD instantons over ALE spaces to flat bundles on $G_{2}$ –orbifolds of the form $T^{7} ∕ Γ$ . We use this construction to produce non-trivial examples of $G_{2}$ –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

Volume 17, issue 4 (2013)