Nonrepetitive colorings of graphs excluding a fixed immersion or topological minor

We prove that graphs excluding a fixed immersion have bounded nonrepetitive chromatic number. More generally, we prove that if H is a fixed planar graph that has a planar embedding with all the vertices with degree at least 4 on a single face, then graphs excluding H as a topological minor have bounded nonrepetitive chromatic number. This is the largest class of graphs known to have bounded nonrepetitive chromatic number