Abstract: By combining algorithms developed separately by Lackenby and Jaco, we provide an algorithm to construct 1-efficient triangulations for all but at most finitely many possible Dehn fillings of a specified triangulated knot manifold. This relies heavily notion of triangulated Dehn fillings developed by Jaco to have control over the normal surfaces added during the filling. After discussing some relevant background, I will describe how this method works and what triangulations it can be applied to.
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