Branched covering
= Branched covering
{wiki=Branched_cover}
= Branched cover
{synonym}
A branched covering is a map that is a <covering space> away from a branch set and has a specified local covering model at that set. For a smooth two-fold covering branched over a codimension-two submanifold, the local model is $(z,u)\mapsto(z^2,u)$. A <two-fold branched cover of a knot> is the basic three-dimensional example.