Instantons on multi-Taub-NUT spaces. I: Asymptotic form and index theorem
type: Item
instance of: scholarly article
title: Instantons on multi-Taub-NUT spaces. I: Asymptotic form and index theorem
zbMATH Open document ID: 1498.53036
author: Sergey A. Cherkis
author: Mark Stern
author: Andrés Larraín-Hubach
published in: Journal of Differential Geometry
publication date: 2022-02-01T00:00:00Z
full work available at URL: https://arxiv.org/abs/1608.00018
full work available at URL: 1631124166.full
review text: In the paper under review the authors study the finite action of an anti-self-dual Yang-Mills connections on the multi-Taub-NUT space. Under a technical assumption the curvature and the harmonic spinor decay rates are established and the index of the associated Dirac operator is computed. The authors claim that this paper is the first in a series of papers proving the completeness of the bow construction of instantons on multi-Taub-NUT spaces and exploring it in detail. The analysis provided within the paper assumes a generic asymptotic holonomy condition: there exists a ray in the base \(\mathbb{R}^3\) such that the holonomy of the instanton connection around every circle fiber over that ray is generic (i.e., belongs to a common compact subset of the regular \(\mathrm{U} (n)\) adjoint orbit). More precisely, the authors assume that the eigenvalues of the holonomy over some ray in the base \(\mathbb{R}^3\) are distinct with the distance between distinct eigenvalues bounded below by a positive constant.
reviewed by: Adrian Sandovici
Mathematics Subject Classification ID: 53C07
Mathematics Subject Classification ID: 58E15
zbMATH DE Number: 7467756
zbMATH Keywords: anti-self-dual Yang-Mills connections
zbMATH Keywords: multi-Taub-NUT space
zbMATH Keywords: generic asymptotic holonomy
zbMATH Keywords: curvature and harmonic spinor decay rates
zbMATH Keywords: index of Dirac operator
MaRDI profile type: Publication
OpenAlex ID: W3198996104
arXiv ID: 1608.00018
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Wikidata QID: Q115164246
DOI: 10.4310/JDG/1631124166
description: scientific article