论文标题
地球电流的双空间
Dual spaces of geodesic currents
论文作者
论文摘要
双曲线表面上的每个测量电流都有相关的双空间。如果电流是层压板，则该双重嵌入方式将其嵌入真实树中。我们表明，一般而言，双重空间是Gromov双曲线树级别的空间，并用大地测量电流表示其Gromov双曲线常数。对于没有原子和全部支持的大地电流，例如来自某些较高等级表示的电流，我们表明双重表面对表面是同质的。我们还分析了双重表面基本组的双重和性能的完整性。此外，我们比较了双重空间中的两个自然拓扑。
Every geodesic current on a hyperbolic surface has an associated dual space. If the current is a lamination, this dual embeds isometrically into a real tree. We show that, in general, the dual space is a Gromov hyperbolic metric tree-graded space, and express its Gromov hyperbolicity constant in terms of the geodesic current. In the case of geodesic currents with no atoms and full support, such as those coming from certain higher rank representations, we show the duals are homeomorphic to the surface. We also analyze the completeness of the dual and the properties of the action of the fundamental group of the surface on the dual. Furthermore, we compare two natural topologies in the space of duals.
