Surgery is the process of deleting some subset of a manifold and gluing it back in such a way as to obtain a different manifold. In this talk, we'll construct some interesting 3-manifolds via surgery on knots and links in the 3-sphere, and we'll show that every compact, orientable 3-manifold can be obtained in this fashion. We'll also discuss the connections between surgery and 4-manifolds. Time permitting, we'll look at how modern 3-manifold invariants (such as Heegaard Floer homology) behave under surgeries. Some basic knowledge of topology is helpful, but all are welcome.
This talk should be accesible to everyone -- elementary topology required.