论文标题
抛物线式希格斯束和循环单极链
Parabolic Higgs bundles and cyclic monopole chains
论文作者
论文摘要
我们在SU（2）单极链和``频谱数据''之间制定了对应关系，由$ \ Mathbb {cp}^1 \ times \ times \ mathbb {cp}^1 $组成。这是唐纳森单孔协会与理性地图的单极链的类似物。该结构基于NAHM变换，该变换将单极链与圆柱体上的Higgs捆绑在一起。作为一个应用程序，我们将收费$ k $单极链分类为$ \ mathbb {z} _ {2k} $不变。我们介绍了使用数值NAHM变换构建的这些对称单极链的图像。
We formulate a correspondence between SU(2) monopole chains and ``spectral data'', consisting of curves in $\mathbb{CP}^1\times\mathbb{CP}^1$ equipped with parabolic line bundles. This is the analogue for monopole chains of Donaldson's association of monopoles with rational maps. The construction is based on the Nahm transform, which relates monopole chains to Higgs bundles on the cylinder. As an application, we classify charge $k$ monopole chains which are invariant under actions of $\mathbb{Z}_{2k}$. We present images of these symmetric monopole chains that were constructed using a numerical Nahm transform.
