G2–instantons over asymptotically cylindrical manifolds

Sá Earp, Henrique

doi:10.2140/gt.2015.19.61

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$G_2$–instantons over asymptotically cylindrical manifolds

Henrique N Sá Earp

Geometry & Topology 19 (2015) 61–111

DOI: 10.2140/gt.2015.19.61

Abstract

A concrete model for a $7$ –dimensional gauge theory under special holonomy is proposed, within the paradigm of Donaldson and Thomas, over the asymptotically cylindrical $G_{2}$ –manifolds provided by Kovalev’s solution to a noncompact version of the Calabi conjecture.

One obtains a solution to the $G_{2}$ –instanton equation from the associated Hermitian Yang–Mills problem, to which the methods of Simpson et al are applied, subject to a crucial asymptotic stability assumption over the “boundary at infinity”.

Keywords

gauge theory, $G_2$–instantons

Mathematical Subject Classification 2010

Primary: 53C07

Secondary: 58J35, 53C29

References

Publication

Received: 6 April 2012

Revised: 9 April 2014

Accepted: 10 May 2014

Published: 27 February 2015

Proposed: Ronald Stern

Seconded: Ciprian Manolescu, Richard Thomas

Authors

Henrique N Sá Earp
Imperial College London London SW7 2AZ UK	Universidade Estadual de Campinas (Unicamp) São Paulo Brazil
http://www.ime.unicamp.br/~hqsaearp

Volume 19, issue 1 (2015)