Before revision:  in particular, there is a variety of problems in computational 3-manifold topology---some of them known to be computationally hard in general---that become solvable in polynomial time as soon as the dual graph of the input triangulation has bounded treewidth.
After revision:  in particular, there is a variety of problems in computational 3-manifold topology - some of them known to be computationally hard in general---that become solvable in polynomial time as soon as the dual graph of the input triangulation has bounded treewidth.