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arXiv · 2311.08378

New examples of $G_2$-instantons on $\mathbb{R}^4 \times S^3$

Izar Alonso
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Abstract

We study the existence of $\text{SU}(2)^2$-invariant $G_2$-instantons on $\mathbb{R}^4 \times S^3$ with the coclosed $G_2$-structures found on [arXiv:2209.02761]. We find an explicit 1-parameter family of $\text{SU}(2)^3$-invariant $G_2$-instantons on the trivial bundle on $\mathbb{R}^4 \times S^3$ and study its ''bubbling'' behaviour. We prove the existence a 1-parameter family on the identity bundle. We also provide existence results for locally defined $\text{SU}(2)^2$-invariant $G_2$-instantons.

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Izar Alonso. 2023-11-14. New examples of $G_2$-instantons on $\mathbb{R}^4 \times S^3$. https://doi.org/10.1016/j.geomphys.2024.105292

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