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# Mathematical Research Letters

## Volume 23 (2016)

### Number 2

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

Pages: 529 – 544

DOI: https://dx.doi.org/10.4310/MRL.2016.v23.n2.a11

#### Author

#### Abstract

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].

#### Keywords

$\mathrm{G}_2$–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