Ergodic solenoidal homology: Realization theorem

Abstract

We define generalized currents associated with immersions of abstract oriented 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.

16 pages. The paper arXiv:math/0702501 has been divided into three parts. The first two parts are arXiv:0910.2836 and arXiv:0910.2837. This paper corresponds to the third part and contains the main result of arXiv:math/0702501