Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Any closed orientable 3-manifold can be realized by removing a neighborhood of a link in the 3-sphere and gluing in solid tori. Moreover, although this realization is not unique, any two such can be related by a sequence of a few moves, called Kirby moves. After giving an elementary introduction to knots and 3-manifolds, I will sketch a proof of these two statements that uses Heegaard splittings. In particular, there will be no 4- or 5-manifolds in this talk. No background necessary!