论文标题
$ g $ -Instanton Moduli空间上的索引和方向的定位
Localization of indices and orientations on $G$-instanton moduli spaces
论文作者
论文摘要
乔伊斯（Joyce），田中（Tanaka）和Upmeier在封闭的四个歧管上给出了$ g $ -Instanton Moduli空间的方向，该歧管使用$ 4 $ -MANIFOLD上的$ \ Mathrm {spin}^c $结构在规范上定义。在本说明中，我们描述了$ \ mathrm {spin}^c $结构的其他选择给出的方向之间的关系。此外，我们通过使用Witten定位Dirac Type Operator的索引，提供了Instanton Moduli空间的方向性的替代证明，以及乔伊斯（Joyce），田中和Upmeier的方向的替代构造。
Joyce, Tanaka, and Upmeier give an orientation of the $G$-instanton moduli spaces on a closed four manifolds which is canonically defined using the the $\mathrm{Spin}^c$ structure on the $4$-manifold. In this note, we describe the relation between the orientations given by other choices of the $\mathrm{Spin}^c$ structures, in a slightly more general setting. Furthermore, we give an alternative proof of the orientability of the instanton moduli spaces and an alternative construction of the orientation by Joyce, Tanaka and Upmeier, by using Witten localization of the index of a Dirac type operator.
