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 . A two-fold branched cover of a knot is the basic three-dimensional example.
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A branched covering is a concept in topology, specifically in the study of covering spaces. It refers to a specific type of continuous surjective map between two topological spaces, typically between manifolds or Riemann surfaces, which behaves like a covering map except for certain points, called branch points, where the behavior is more complicated.