I don't know! Systems where there are rigid notions of angle, distance and position are generally thought to be geometric, not topological. However, often a topological viewpoint can be useful even in solving geometric problems, e.g. circuit autorouting. What are the outstanding problems in unwrapping 3d models (I have no idea what that is) / texture projection?
cottonseed -- do you have a dummy email address at which I can contact you? I work for a startup that leverages topology for data analysis, and we are hiring.
