Protected spin characters, link invariants, and q-nonabelianization

In this talk I will describe a new link "invariant" (with certain wall-crossing properties) for links L in a three-manifold M, where M takes the form of a surface times the real line. This link "invariant" is constructed via a map, called the q-nonabelianization map, from the
gl(N) skein algebra of M to the gl(1) skein algebra of a covering three-manifold M'. In the special case of M=R^3, this map computes well-known link invariants in a new way. As a physical application, the q-nonabelianization map computes protected spin character counting BPS ground states with spin for line defects in 4d N=2 theories of class-S. I will also mention possible extension to more general three-manifolds, as well as further physical applications to class-S theories. This talk is based on joint work with Andrew Neitzke, and ongoing work with Gregory Moore and Andrew Neitzke.