Lifting Surgeries to Branched Covering Spaces
Lifting Surgeries to Branched Covering Spaces
It is proved that if ${M^n}$ is a branched covering of a sphere, branched over a manifold, so is ${M^n} \times {S^m}$, but the number of sheets is one more. In particular, the n-dimensional torus is an n-fold simple covering of ${S^n}$ branched over an orientable manifold. The proof involves …