不可定向曲面上的Goldman流动
Goldman flows on a nonorientable surface
摘要：
给定任意曲面中的嵌入圆柱，给出了相应的Goldman流的规范论定义，Goldman流是曲面上平坦SU（2）-联络等价类的模空间的稠密开子集上的圆作用.在一个紧凑的不可定向曲面上的圆柱体上升为在可定向双层罩上的两个圆柱体，“合成流”是其中一个相关流与另一个相关流的反向流的合成。给出了明确的描述，我们将不可定向曲面模空间上的流与双覆盖模空间上的复合流联系起来。证明了复合流保持一定的拉格朗日子流形。
英文摘要：
Given an embedded cylinder in an arbitrary surface, we give a gauge theoretic definition of the associated Goldman flow, which is a circle action on a dense open subset of the moduli space of equivalence classes of flat SU(2)-connections over the surface. A cylinder in a compact nonorientable surface lifts to two cylinders in the orientable double cover, and the "composite flow" is the composition of one of the associated flows with the inverse flow of the other. Providing explicit descriptions, we relate the flow on the moduli space of the nonorientable surface with the composite flow on the moduli space of the double cover. We prove that the composite flow preserves a certain Lagrangian submanifold.
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