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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
$G_2$–instantons over asymptotically cylindrical manifolds

Henrique N Sá Earp

Geometry & Topology 19 (2015) 61–111
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 G2–manifolds provided by Kovalev’s solution to a noncompact version of the Calabi conjecture.

One obtains a solution to the G2–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