Branched Coverings of Manifolds and nH-Spaces

Abstract

We show that on the sphere S^m, m ≠ 1, 3, 7, there exists an n_m-valued multiplication with unit for some n_m ∈ {2, 4, 8}. We also explicitly construct a 2^k−1-fold branched covering of \(S^{m_1}\;\times\cdots\times\;S^{m_k}\) the product S^m1× ··· × S^mk of k spheres over the sphere S^m, m = m₁ + ··· + m_k.