Branched coverings. I

Abstract

This paper analyzes the possible cobordism classes [ M ] − ( deg ϕ ) [ N ] [M] - (\deg \;\phi )[N] for ϕ : M → N \phi : M \to N a smooth branched covering of closed smooth manifolds. It is assumed that the branch set is a codimension 2 2 submanifold. The results are a fairly complete description in the unoriented case, a partial description in the oriented case, and a detailed analysis of the case in which N N is a sphere.