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<p>In this paper we compute the deformations of the Clarke–Oliveira instantons on the Bryant–Salamon <i>Spin</i>(7)-Manifold. The Bryant–Salamon <i>Spin</i>(7)-Manifold — the negative spinor bundle of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11040_2025_9522_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(S^4\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>S</mi> <mn>4</mn> </msup> </math></EquationSource> </InlineEquation> — is an asymptotically conical manifold where the link is the squashed 7-sphere. We use the deformation theory developed by the author in a previous paper to calculate the deformations of the Clarke–Oliveira instantons and calculate the virtual dimensions of the moduli spaces.</p>

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Deformations of Clarke–Oliveira Instantons on Bryant–Salamon Spin(7)-Manifold

  • 期刊论文

  • 发表日期：

    2025年8月20日

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  • Tathagata Ghosh

摘要

In this paper we compute the deformations of the Clarke–Oliveira instantons on the Bryant–Salamon Spin(7)-Manifold. The Bryant–Salamon Spin(7)-Manifold — the negative spinor bundle of \(S^4\) S 4 — is an asymptotically conical manifold where the link is the squashed 7-sphere. We use the deformation theory developed by the author in a previous paper to calculate the deformations of the Clarke–Oliveira instantons and calculate the virtual dimensions of the moduli spaces.