## Abstract

We propose a method to construct G
_{2}-instantons over a compact twisted connected sum G
_{2}-manifold, applying a gluing result of Sá Earp and Walpuski to instantons over a pair of 7-manifolds with a tubular end. In our example, the moduli spaces of the ingredient instantons are non-trivial, and their images in the moduli space over the asymptotic cross-section K3 surface intersect transversely. Such a pair of asymptotically stable holomorphic bundles is obtained using a twisted version of the Hartshorne-Serre construction, which can be adapted to produce other examples. Moreover, their deformation theory and asymptotic behaviour are explicitly understood, results which may be of independent interest.

Original language | English |
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Pages (from-to) | 471-509 |

Number of pages | 39 |

Journal | Mathematical Research Letters |

Volume | 28 |

Issue number | 2 |

DOIs | |

Publication status | Published - 13 May 2021 |

### Bibliographical note

Funding Information:We thank Daniele Faenzi, Marcos Jardim and Thomas Walpuski for many important discussions. In particular, we acknowledge Marcos Jardim for suggesting the Hartshorne-Serre technique to produce bundles parametrised by curves. GM is supported by grant 2014/05733-9, São Paulo Research Foundation (Fapesp), and the Marco Brunella Grant of Burgundy University. HSE is supported by grant 2014/24727-0, São Paulo Research Foundation (Fapesp), and the Brazilian National Council for Scientific and Technological Development (CNPq) Productivity Grant 312390/2014-9. JN is supported by the Simons Foundation under the Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics (grant #488631, Johannes Nordström).

## ASJC Scopus subject areas

- General Mathematics