Geometric topology is the study of manifolds, maps between manifolds, and embeddings of manifolds in one another. Included in this sub-branch of Pure Mathematics; knot theory, homotopy, manifold theory, surgery theory, and other topics are developed in extensive detail. Do you happen to know of any applications of the techniques and/or theorems from geometric topology to theoretical physics? I'm guessing that most applications are in topological quantum field theory. Does anyone know of some specific (I'm asking for technical details) uses of say, whitney tricks, casson handles, or anything from surgery theory?
If you cannot give a full response, references to relevant literature would work as well.