遍历螺线管同调
Ergodic solenoidal homology
摘要：
我们定义了广义电流与浸入的抽象的横截措施。我们实现了几何上的完整的实同调的紧致流形与这些广义电流，更准确地说，与浸入的最小唯一遍历。这使得精确和几何德拉姆的实同调的实现，只使用一个限制几何子类的电流。这些广义电流确实扩展了Ruelle-Sullivan电流和Schwartzman电流。我们扩展Schwartzman理论超越1维，并提供了一个统一的治疗Ruelle-Sullivan和Schwartzman理论通过Birkhoff的遍历定理的类浸入控制的控制。我们开发了一些相交理论，这些新的广义电流，解释了为什么实现定理不能实现只有与Ruelle-Sullivan电流。
英文摘要：
We define generalized currents associated with immersions of abstract solenoids with a transversal measure. We realize geometrically the full real homology of a compact manifold with these generalized currents, and more precisely with immersions of minimal uniquely ergodic solenoids. This makes precise and geometric De Rham's realization of the real homology by only using a restricted geometric subclass of currents. These generalized currents do extend Ruelle-Sullivan and Schwartzman currents. We extend Schwartzman theory beyond dimension 1 and provide a unified treatment of Ruelle-Sullivan and Schwartzman theories via Birkhoff's ergodic theorem for the class of immersions of controlled solenoids. We develop some intersection theory of these new generalized currents that explains why the realization theorem cannot be achieved only with Ruelle-Sullivan currents.
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