Branched Coverings of Manifolds and nH-Spaces

摘要

We show that on the sphere S-m, m not equal 1, 3, 7, there exists an n(m)-valued multiplication with unit for some n(m) is an element of {2, 4, 8}. We also explicitly construct a 2(k-1)-fold branched covering of Sm1Smk the product S(m1)x x S-mk of k spheres over the sphere S-m, m = m(1) + + m(k).