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Instantons on multi-Taub-NUT Spaces III: Down Transform, Completeness, and Isometry

Sergey A. Cherkis, Andrés Larraín-Hubach, Mark Stern · 2023 · math.DG · DOI 10.48550/arxiv.2308.02048 · arXiv 2308.02048

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abstract

The index bundle of a family of Dirac operators associated to an instanton on a multi-Taub-NUT space forms a bow representation. We prove that the gauge equivalence classes of solutions of this bow representation are in one-to-one correspondence with the instantons. We also prove that this correspondence establishes an isometry of the bow and instanton moduli spaces.

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2026 1

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  • Obstructions to Spin(7) Nahm transforms on tori math.DG · 2026-07-30 · accept · none · ref 9 · internal anchor

    Spin(7) Nahm transforms on 8-tori lack generic vanishing, and asymptotic holonomy of highly twisted instantons need not be Spin(7).