Inserted: 29 jan 2002
Journal: Ann. Global Anal. Geom.
We derive an approximation of codimension-one integral cycles (and cycles modulo $p$) in a compact riemannian manifolds by means of piecewise regular cycles: we obtain both flat convergence, and convergence of the masses. The theorem is proved by using suitable principal bundles with discrete group. As a byproduct, we give an alternative proof of the main results in BO1, BO2, which does not use the regularity theory for homology minimizers in a riemannian manifold. This gives also a result of $\Gamma$-convergence.
Keywords: Geometric measure theory, minimal surfaces, $\Gamma$ - convergence, homology groups, fiber bundles