Description

Faculty Mentor: Carmen Rovi

Suppose M is a closed manifold which can be cut open along a codimension 1 submanifold. By doing this cutting operation we obtain two manifolds with the same boundary which we can now glue back together using an automorphism of the boundary which is not the identity. The new object that we obtain is said to be "cut and paste" or SK-equivalent to the manifold M we started with. It turns out that the cut and paste operation doesn't only define an equivalence relation, it defines certain groups called the SK-groups. The SK-groups were first defined some 40 years ago, but they haven't been developed or investigated in depth since then, even though they have interesting connections with very active areas of research. An interesting topic is to understand which topological invariants are invariants of the cut and paste operation. The goal of this project will be to describe which cut and paste invariants are partition functions of topological quantum field theories.