论文标题
$ \ mathrm {g} _2 $ -instantons在7-phere上
$\mathrm{G}_2$-instantons on the 7-sphere
论文作者
论文摘要
我们研究了7-Sphere上的$ \ mathrm {g} _2 $ -Instants的变形理论，特别是通过Quaternionic Hopf纤维纤维从4-Sphere上获得的instantons的变形理论。我们发现，标准ASD Instanton的回调在于一个平滑，完整的，15维的家族$ \ Mathrm {G} _2 $ -Instantons。通常，$ s^7 $上的无穷小$ \ mathrm {g} _2 $ -instanton变形的空间被标识为$ s^4上的ASD变形的三个副本。
We study the deformation theory of $\mathrm{G}_2$-instantons on the 7-sphere, specifically those obtained from instantons on the 4-sphere via the quaternionic Hopf fibration. We find that the pullback of the standard ASD instanton lies in a smooth, complete, 15-dimensional family of $\mathrm{G}_2$-instantons. In general, the space of infinitesimal $\mathrm{G}_2$-instanton deformations on $S^7$ is identified with three copies of the space of ASD deformations on $S^4.$
