Braids and branched coverings of dimension three

We study simple branched coverings of degree d of the 2- and 3- dimensional sphere branched over oriented links. We demonstrate how to use braid charts to develop embeddings of these into $S^k \times D^2$ for $k=2,3 when$d=2,3$. This is an initial part of our study and represents the manuscript submitted to the RIMS workshop at Intelligence of Low Dimensional Topology.