Framed Combinatorial Topology, an illustrated tour

Do you have a favorite smooth manifold? Would you like a combinatorial model of it? Then embed it in euclidean space and wiggle it suitably. The result is called a tame tangle. We show that such generic embeddings are classified (up to framed ambient homeomorphism) by a combinatorial structure called a tangle truss. We hypothesize that suitable wiggles always exist and that the resulting tangle truss faithfully encodes the smooth structure of the manifold.

I will give a light and informal overview of framed combinatorial topology (gradually working up to tame tangles and tangle trusses), illustrated by images from a new book on the subject, with Christoph Dorn.