Mathematical Research Letters

Volume 23 (2016)

Number 2

$\mathrm{G}_2$–instantons over twisted connected sums: An example

Pages: 529 – 544



Thomas Walpuski (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)


Using earlier work of Sá Earp and the author [SEW15] we construct an irreducible unobstructed $\mathrm{G}_2$–instanton on an $\mathrm{SO}(3)$–bundle over a twisted connected sum $\mathrm{G}_2$–manifold recently discovered by Crowley and Nordström [CN14].


$\mathrm{G}_2$–manifolds, $\mathrm{G}_2$–instantons, twisted connected sum, gauge theory, holomorphic bundles, gluing construction

2010 Mathematics Subject Classification

53C07, 53C25, 53C38

Accepted 22 October 2015

Published 6 June 2016