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arXiv · 2310.03451

Spin(7)-instantons on Joyce's first examples of compact Spin(7)-manifolds

Mateo Galdeano·Daniel Platt·Yuuji Tanaka·Luya Wang
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Abstract

We construct $Spin(7)$-instantons on one of Joyce's compact $Spin(7)$-manifolds. The underlying compact $Spin(7)$-manifold given by Joyce is the same as in Lewis' construction of $Spin(7)$-instantons. However, our construction method and the resulting instantons are new. The compact $Spin(7)$-manifold is constructed by gluing a $Spin(7)$-orbifold and certain local model spaces around the orbifold singularities. We construct our instantons by gluing non-flat connections on the local model spaces to a flat connection on the $Spin(7)$-orbifold. We deliver more than $20,000$ new four-parameter families of examples of $Spin(7)$-instantons within the structure groups $SO(3), SO(4), SO(5), SO(7)$, and $SO(8)$.

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Mateo Galdeano, Daniel Platt, Yuuji Tanaka, Luya Wang. 2023-10-05. Spin(7)-instantons on Joyce's first examples of compact Spin(7)-manifolds. https://arxiv.org/abs/2310.03451

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