关于Riemann surfaces上Abel微分诱导流不变量的注记
A note on invariants of flows induced by Abelian differentials on Riemann surfaces
摘要：
紧致黎曼曲面上任意阿贝尔微分的实部和虚部定义了紧致可定向$C^\infty$曲面上的两个流。此外，这些流通过Poincaré递推在每一条横截简单闭曲线上引起区间交换变换。本文证明了几个自然地与其中一个流相关联的$C^\ast$代数的有序$K_0$群分别是：区间交换变换是同构的，主要使用I.帕特南
英文摘要：
The real and imaginary part of any Abelian differential on a compact Riemann surface define two flows on the underlying compact orientable $C^\infty$ surface. Furthermore, these flows induce an interval exchange transformation on every transversal simple closed curve, via Poincaré recurrence. This note shows that the ordered $K_0$ groups of several $C^\ast$ algebras naturally associated to one of the flows resp. interval exchange transformations are isomorphic, mainly using methods of I. Putnam.
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