A resolution theorem for homology cycles of real algebraic varieties (Q1060257)

The proof of the following result is given. Let V be a compact nonsingular real algebraic set. Then there exists an algebraic resolution \(\pi\) : \(\tilde V\to V\) such that \(H_ k(\tilde V;{\mathbb{Z}}_ 2)\) is generated by components of k-dimensional compact nonsingular algebraic subsets (precisely, stable algebraic subsets of \(\tilde V\) for all k. - The reason for this result not to be a direct consequence of Hironaka's resolution theorem is that not all homology cycles of V may be represented by algebraic subsets.