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

Karsten Matthies; Johannes Nordström; Matt Turner

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
Journal	Communications in Analysis & Geometry
Publication status	Acceptance date - 29 Jun 2023

Bibliographical note

28 pages, 6 figures, 1 table

Keywords

math.DG
math.DS
53C07, 53C25

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2202.05028v1Submitted manuscript, 355 KB

https://arxiv.org/abs/2202.05028v3Licence: Other

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

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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PY - 2023/6/29

Y1 - 2023/6/29

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.

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KW - math.DS

KW - 53C07, 53C25

M3 - Article

SN - 1019-8385

JO - Communications in Analysis & Geometry

JF - Communications in Analysis & Geometry

ER -

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

Abstract

Bibliographical note

Keywords

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Cite this