SU(2)^2xU(1)-invariant G_2-instantons on the AC limit of the C7 family

Karsten Matthies; Johannes Nordström; Matt Turner

doi:10.4310/CAG.241212034215

SU(2)^2xU(1)-invariant G_2-instantons on the AC limit of the C7 family

Karsten Matthies, Johannes Nordström, Matt Turner

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Abstract

We construct SU(2)^2xU(1)-invariant G_2-instantons on the asymptotically conical limit of the C7 family of G_2-metrics. The construction uses a dynamical systems approach involving perturbations of an abelian solution and a solution on the G_2-cone. From this we obtain a 1-parameter family of invariant instantons with gauge group SU(2) and bounded curvature.

Original language	English
Pages (from-to)	2505-2549
Journal	Communications in Analysis & Geometry
Volume	32
Issue number	9
DOIs	https://doi.org/10.4310/CAG.241212034215
Publication status	Published - 11 Dec 2024

Keywords

math.DG
math.DS
53C07, 53C25

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10.4310/CAG.241212034215

2202.05028v1Submitted manuscript, 355 KB

https://arxiv.org/abs/2202.05028v3

Cite this

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abstract = "We construct SU(2)^2xU(1)-invariant G_2-instantons on the asymptotically conical limit of the C7 family of G_2-metrics. The construction uses a dynamical systems approach involving perturbations of an abelian solution and a solution on the G_2-cone. From this we obtain a 1-parameter family of invariant instantons with gauge group SU(2) and bounded curvature. ",

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AU - Nordström, Johannes

AU - Turner, Matt

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Y1 - 2024/12/11

N2 - We construct SU(2)^2xU(1)-invariant G_2-instantons on the asymptotically conical limit of the C7 family of G_2-metrics. The construction uses a dynamical systems approach involving perturbations of an abelian solution and a solution on the G_2-cone. From this we obtain a 1-parameter family of invariant instantons with gauge group SU(2) and bounded curvature.

AB - We construct SU(2)^2xU(1)-invariant G_2-instantons on the asymptotically conical limit of the C7 family of G_2-metrics. The construction uses a dynamical systems approach involving perturbations of an abelian solution and a solution on the G_2-cone. From this we obtain a 1-parameter family of invariant instantons with gauge group SU(2) and bounded curvature.

KW - math.DG

KW - math.DS

KW - 53C07, 53C25

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DO - 10.4310/CAG.241212034215

M3 - Article

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JO - Communications in Analysis & Geometry

JF - Communications in Analysis & Geometry

IS - 9

ER -

SU(2)^2xU(1)-invariant G_2-instantons on the AC limit of the C7 family

Abstract

Keywords

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