Examples of deformed G2-instantons/Donaldson–Thomas connections
Annales de l'Institut Fourier, Volume 72 (2022) no. 1, pp. 339-366.

In this note, we provide the first non-trivial examples of deformed G 2 -instantons, originally called deformed Donaldson–Thomas connections. As a consequence, we see how deformed G 2 -instantons can be used to distinguish between nearly parallel G 2 -structures and isometric G 2 -structures on 3-Sasakian 7-manifolds. Our examples give non-trivial deformed G 2 -instantons with obstructed deformation theory and situations where the moduli space of deformed G 2 -instantons has components of different dimensions. We finally study the relation between our examples and a Chern–Simons type functional which has deformed G 2 -instantons as critical points.

Dans cette note, nous fournissons les premiers exemples non triviaux de G 2 -instantons déformés, initialement appelés connexions Donaldson–Thomas déformées. En conséquence, on peut utiliser G 2 -instantons déformés pour faire la distinction entre des G 2 -structures presque parallèles et des G 2 -structures isométriques sur des 7-variétés 3-Sasakiennes. Nos exemples donnent des G 2 -instantons déformés non triviaux avec une théorie de la déformation obstruée et des situations où l’espace des modules des G 2 -instantons déformés a des composantes de dimensions différentes. Nous étudions enfin la relation entre nos exemples et une fonctionnelle de type Chern–Simons qui a les G 2 -instantons déformés en points critiques.

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DOI: 10.5802/aif.3465
Classification: 53C07, 53C25
Keywords: Deformed $\mathrm{G}_2$-instantons, deformed Donaldson–Thomas connections, nearly parallel $\mathrm{G}_2$-structures, isometric $\mathrm{G}_2$-structures, 3-Sasakian.
Mot clés : $\mathrm{G}_2$-instantons déformés, connexions Donaldson–Thomas déformés, $\mathrm{G}_2$-structures presque parallèles, $\mathrm{G}_2$-structures isométriques, 3-Sasakien.
Lotay, Jason D. 1; Oliveira, Gonçalo 2

1 University of Oxford, U.K.
2 Universidade Federal Fluminense IME-GMA Niterói, Brazil
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Lotay, Jason D.; Oliveira, Gonçalo. Examples of deformed G2-instantons/Donaldson–Thomas connections. Annales de l'Institut Fourier, Volume 72 (2022) no. 1, pp. 339-366. doi : 10.5802/aif.3465. https://aif.centre-mersenne.org/articles/10.5802/aif.3465/

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