Stokes流形与簇代数
Stokes manifolds and cluster algebras
摘要：
斯托克斯流形，也被称为野特征簇，具有自然的辛结构。我们的目标是提供明确的对数正则坐标的这些自然泊松结构的斯托克斯流形上的多项式连接的秩$2$，从而包括第二Painlevé\层次。这种构造提供了泊松结构的显式线性化，该结构首先由Flaschka和Newell发现，然后由Boalch重新发现和推广。我们证明了，对于度为$K$的联络，Stokes流形是$A_{2K}$型的簇流形.的主要思想，然后应用明确表达的日志-正则坐标的泊松括号介绍了乌加利亚的背景下Frobenius流形，然后也适用于Bondal的研究辛广群的二次型。
英文摘要：
Stokes' manifolds, also known as wild character varieties, carry a natural symplectic structure. Our goal is to provide explicit log-canonical coordinates for these natural Poisson structures on the Stokes' manifolds of polynomial connections of rank $2$, thus including the second Painlevé\ hierarchy. This construction provides the explicit linearization of the Poisson structure first discovered by Flaschka and Newell and then rediscovered and generalized by Boalch. We show that, for a connection of degree $K$, the Stokes' manifold is a cluster manifold of type $A_{2K}$. The main idea is then applied to express explicitly also the log--canonical coordinates for the Poisson bracket introduced by Ugaglia in the context of Frobenius manifolds and then also applied by Bondal in the study of the symplectic groupoid of quadratic forms.
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