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arXiv · 1510.03836

Construction of G_2-instantons via twisted connected sums

Grégoire Menet·Johannes Nordström·Henrique N. Sá Earp
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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 (see arXiv:1310.7933). 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.

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Grégoire Menet, Johannes Nordström, Henrique N. Sá Earp. 2019-10-31. Construction of G_2-instantons via twisted connected sums. https://doi.org/10.4310/mrl.2021.v28.n2.a6

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