标题： 奇异瞬子与庞加莱六次方程 显示英文标题

标题： Singular Instantons and Painlevé VI

摘要： 我们考虑一个双参数的瞬子族，该族在[Sadun L., Comm. Math. Phys. 163 (1994), 257-291]中被研究，它在${\rm SU}_2$在$S^4$上的不可约作用下保持不变，但这些瞬子并不是全局定义的。 我们将看到这些瞬子会产生一个单参数的 Painlevé VI 方程族（$\text{P}_{\text{VI}}$）的解，并且我们将给出瞬子与$\text{P}_{\text{VI}}$的解之间的显式映射。 这些解只有在参数取对应于可以扩展到整个$S^4$的瞬子的值时才是代数的。 这项工作是对[Muñiz Manasliski R., Contemp. Math., Vol. 434, Amer. Math. Soc., Providence, RI, 2007, 215-222]和[Muñiz Manasliski R., J. Geom. Phys. 59 (2009), 1036-1047, arXiv:1602.07221]的推广，在这些工作中研究了没有奇点的瞬子。 显示英文摘要

摘要： We consider a two parameter family of instantons, which is studied in [Sadun L., Comm. Math. Phys. 163 (1994), 257-291], invariant under the irreducible action of ${\rm SU}_2$ on $S^4$, but which are not globally defined. We will see that these instantons produce solutions to a one parameter family of Painlev\'e VI equations ($\text{P}_{\text{VI}}$) and we will give an explicit expression of the map between instantons and solutions to $\text{P}_{\text{VI}}$. The solutions are algebraic only for that values of the parameters which correspond to the instantons that can be extended to all of $S^4$. This work is a generalization of [Mu\~niz Manasliski R., Contemp. Math., Vol. 434, Amer. Math. Soc., Providence, RI, 2007, 215-222] and [Mu\~niz Manasliski R., J. Geom. Phys. 59 (2009), 1036-1047, arXiv:1602.07221], where instantons without singularities are studied.