We seek to develop the Casson-Lin invariants using Chern-Simons gauge theory. This approach should allow us to give a more general definition of the invariants. We seek to perform computations of the invariants in various cases, and to understand what information the invariants carry. The special case of SU(2) suggests the SU(n) Casson-Lin invariants might be invariant under link homotopy, and we hope to shed light on that question.
Impact
The SU(n) Casson-Lin invariants have been defined for links in S^3 using braids and projective representations. This project aims to provide a practical methods fro computing the invariants in examples, such as the Borromean rings.
