Algorithms on braids and links in 3-manifolds

In this thesis, the results of Cattabriga-Gabrovsek regarding the equivalence of links in 3-manifolds will be extended to include genus two 3-manifolds, Dunwoody and Takahashi manifolds. The problem of transitioning from a link’s representation via plat closure of a braid to a representation via standard closure of a braid in the cases of S3, handlebodies, and thickened surfaces will be addressed and solved. The solutions to these problems will be accompanied by C++ programs that implement the algorithms described.