[Exemples de G2-instantons/connexions de Donaldson–Thomas déformées]
Dans cette note, nous fournissons les premiers exemples non triviaux de -instantons déformés, initialement appelés connexions Donaldson–Thomas déformées. En conséquence, on peut utiliser -instantons déformés pour faire la distinction entre des -structures presque parallèles et des -structures isométriques sur des 7-variétés 3-Sasakiennes. Nos exemples donnent des -instantons déformés non triviaux avec une théorie de la déformation obstruée et des situations où l’espace des modules des -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 -instantons déformés en points critiques.
In this note, we provide the first non-trivial examples of deformed -instantons, originally called deformed Donaldson–Thomas connections. As a consequence, we see how deformed -instantons can be used to distinguish between nearly parallel -structures and isometric -structures on 3-Sasakian 7-manifolds. Our examples give non-trivial deformed -instantons with obstructed deformation theory and situations where the moduli space of deformed -instantons has components of different dimensions. We finally study the relation between our examples and a Chern–Simons type functional which has deformed -instantons as critical points.
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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.
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@article{AIF_2022__72_1_339_0,
author = {Lotay, Jason D. and Oliveira, Gon\c{c}alo},
title = {Examples of deformed {G\protect\textsubscript{2}-instantons/Donaldson{\textendash}Thomas} connections},
journal = {Annales de l'Institut Fourier},
pages = {339--366},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {72},
number = {1},
year = {2022},
doi = {10.5802/aif.3465},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3465/}
}
TY - JOUR AU - Lotay, Jason D. AU - Oliveira, Gonçalo TI - Examples of deformed G2-instantons/Donaldson–Thomas connections JO - Annales de l'Institut Fourier PY - 2022 SP - 339 EP - 366 VL - 72 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3465/ DO - 10.5802/aif.3465 LA - en ID - AIF_2022__72_1_339_0 ER -
%0 Journal Article %A Lotay, Jason D. %A Oliveira, Gonçalo %T Examples of deformed G2-instantons/Donaldson–Thomas connections %J Annales de l'Institut Fourier %D 2022 %P 339-366 %V 72 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3465/ %R 10.5802/aif.3465 %G en %F AIF_2022__72_1_339_0
Lotay, Jason D.; Oliveira, Gonçalo. Examples of deformed G2-instantons/Donaldson–Thomas connections. Annales de l'Institut Fourier, Tome 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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