Abstract:
By a classical result in the theory of 3-manifolds known as the Lickorish-Wallace theorem, any closed orientable 3-manifold can be embedded into R³ if a finite number of solid tori are removed from it. In this talk, I will outline the proof of a smooth version of this theorem, where the 3-manifold is assumed to be a smooth manifold and the embedding into R³ is a smooth embedding. I will also describe how instead of removing solid tori it suffices to remove closed curves. This is a joint work with Pekka Pankka and a part of a joint project with Tracey Balehowsky and Matti Lassas.