$$\mathrm{Spin}(7)$$-Instantons from Evolution Equations

Clarke, Andrew; Oliveira, Gonçalo

doi:10.1007/s12220-020-00436-9

Cited by 3 publications

(6 citation statements)

References 27 publications

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“…We can also apply our results to non-trivial complex line bundles when X 7 is the 3-Sasakian Aloff-Wallach space (Corollary 4.12).…”

Section: Resultsmentioning

confidence: 83%

“…-There are infinitely many compact 3-Sasakian 7-manifolds X 7 [3,11]. Key examples are giving by the 7-sphere S 7 and the Aloff-Wallach space SU(3)/ U(1) 1,1 (cf. Example 3.8), which is the SO(3)-frame bundle of Λ 2 + CP 2 .…”

Section: Resultsmentioning

confidence: 99%

“…Remark 1.5. -We recall that, if X 7 is a compact 3-Sasakian 7-manifold, then the metric cone on (X 7 , g ts ) is hyperkähler, and has holonomy Sp (2) if it is not flat, whilst the metric cone on (X 7 , g np ) has holonomy Spin (7).…”

Section: Resultsmentioning

confidence: 99%

“…Remark 4.3. -There are examples of G 2 -instantons on higher rank bundles on X, such as Example 2 in [7], which describes an irreducible G 2instanton with gauge group SO(3) in this setting.…”

Section: G 2 -Instantonsmentioning

confidence: 99%

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Examples of deformed G2-instantons/Donaldson–Thomas connections

Lotay¹,

Oliveira²

2022

Annales De l'Institut Fourier

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In this note, we provide the first non-trivial examples of deformed G 2 -instantons, originally called deformed Donaldson-Thomas connections. As a consequence, we see how deformed G 2 -instantons can be used to distinguish between nearly parallel G 2 -structures and isometric G 2 -structures on 3-Sasakian 7-manifolds. Our examples give non-trivial deformed G 2 -instantons with obstructed deformation theory and situations where the moduli space of deformed G 2 -instantons has components of different dimensions. We finally study the relation between our examples and a Chern-Simons type functional which has deformed G 2 -instantons as critical points.Résumé. -Dans cette note, nous fournissons les premiers exemples non triviaux de G 2 -instantons déformés, initialement appelés connexions Donaldson-Thomas déformées. En conséquence, on peut utiliser G 2 -instantons déformés pour faire la distinction entre des G 2 -structures presque parallèles et des G 2 -structures isométriques sur des 7-variétés 3-Sasakiennes. Nos exemples donnent des G 2 -instantons déformés non triviaux avec une théorie de la déformation obstruée et des situations où l'espace des modules des G 2 -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 G 2 -instantons déformés en points critiques.

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“…We can also apply our results to non-trivial complex line bundles when X 7 is the 3-Sasakian Aloff-Wallach space (Corollary 4.12).…”

Section: Resultsmentioning

confidence: 83%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: G 2 -Instantonsmentioning

confidence: 99%

See 2 more Smart Citations

Examples of deformed G2-instantons/Donaldson–Thomas connections

Lotay¹,

Oliveira²

2022

Annales De l'Institut Fourier

Self Cite

View full text Add to dashboard Cite

show abstract

“…There are examples of G 2 -instantons on higher rank bundles on X, such as Example 2 in [CO20], which describes an irreducible G 2 -instanton with gauge group SO(3) in this setting. 4.2.…”

Section: Remark 43mentioning

confidence: 99%