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<p>We construct <i>Spin</i>(7)-instantons on one of Joyce’s compact <i>Spin</i>(7)-manifolds. The underlying compact <i>Spin</i>(7)-manifold given by Joyce is the same as in Lewis’ construction of <i>Spin</i>(7)-instantons. However, our construction method and the resulting instantons are new. The compact <i>Spin</i>(7)-manifold is constructed by gluing a <i>Spin</i>(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 <i>Spin</i>(7)-orbifold. We deliver more than 20,&#xa0;000 new four-parameter families of examples of <i>Spin</i>(7)-instantons within the structure groups <i>SO</i>(3),&#xa0;<i>SO</i>(4),&#xa0;<i>SO</i>(5),&#xa0;<i>SO</i>(7), and <i>SO</i>(8).</p>

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Spin(7)-Instantons on Joyce’s First Examples of Compact Spin(7)-Manifolds

  • 期刊论文

  • 发表日期：

    2025年10月15日

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  • Mateo Galdeano,
  • Daniel Platt,
  • Yuuji Tanaka,
  • Luya Wang

摘要

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).