Ergodic solenoidal homology: density of ergodic solenoids

Details Ergodic solenoidal homology: density of ergodic solenoids Ergodic solenoidal homology: density of ergodic solenoids

2009-10-19

arxiv.org/abs/0910.3525v1

Australian J. Math. Anal. and Appl. 6 (2009), no. 1, Article 11, 1-8

Mathematics

Differential Geometry

9 pages, 2 figures

Scientific paper

A measured solenoid is a laminated space endowed with a tranversal measure invariant by holonomy, as defined in arXiv:0910.2836. A measured solenoid immersed in a smooth manifold produces a closed current (known as generalized Ruelle-Sullivan current). Uniquely ergodic solenoids are those for which there is a unique (up to scalars) transversal measure. By the results in arXiv:0910.2913, for any smooth manifold, any real homology class is represented by a uniquely ergodic solenoid. In this paper, we prove that the currents associated to uniquely ergodic solenoids are dense in the space of closed currents, therefore proving the abundance of such objects.

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