标题： 对称单极子 显示英文标题

标题： Symmetric Monopoles

摘要： 我们讨论了与任意电荷$SU(2)$Bogomolny 单极子相关的谱曲线和有理映射$k$。 我们描述了关于有理映射所定义平面内反转单极子的效果，并讨论了在这种反转下不变的单极子。 我们定义了强中心单极子，并证明它们构成了$k$-单极子模空间中的测地子流形。 由固定轴上的旋转循环群$C_k$所确定的强中心$k$单极子的空间被证明由若干个旋转曲面组成，推广了 Atiyah 和 Hitchin 在双单极子情况下获得的两个曲面。 这些曲面上的测地线给出了新型的$k$单极子散射。 我们提出了一些在$TP_1$中的曲线，我们推测它们是具有规则固体对称性的单极子的谱曲线。 这些推测基于与 Skyrmions 的类比。 显示英文摘要

摘要： We discuss the spectral curves and rational maps associated with $SU(2)$ Bogomolny monopoles of arbitrary charge $k$. We describe the effect on the rational maps of inverting monopoles in the plane with respect to which the rational maps are defined, and discuss the monopoles invariant under such inversion. We define the strongly centred monopoles, and show they form a geodesic submanifold of the $k$-monopole moduli space. The space of strongly centred $k$-monopoles invariant under the cyclic group of rotations about a fixed axis, $C_k$, is shown to consist of several surfaces of revolution, generalizing the two surfaces obtained by Atiyah and Hitchin in the 2-monopole case. Geodesics on these surfaces give a novel type of $k$-monopole scattering. We present a number of curves in $TP_1$ which we conjecture are the spectral curves of monopoles with the symmetries of a regular solid. These conjectures are based on analogies with Skyrmions.