Roots of Knotted Graphs and Orbifolds

Let G be a graph (1-dimensional CW complex) in a compact 3manifold M . Following [1], we will apply to the pair (M, G) certain simplification moves as long as possible. What we get is a root of (M, G). Our main result is that for any pair (M, G) the root exists and is unique. Similar results hold for graphs with colored edges and for 3-orbifolds, which can… (More)