Culler-Shalen (semi-)norms

Let M be a 3-manifold with boundary consisting of one torus. I will show how Culler and Shalen defined a norm on the (real) Dehn-surgery space R2=H_1(partial M; R) associated to the canonical component of the character variety of M. I will then show how this was generalized by Boyer and Zhang to a semi-norm for other components in the character variety. I will then discuss properties of this (semi-)norm, in particular its relationship to the so-called A-polynomial. I also will discuss some important results regarding exceptional fillings of hyperbolic manifolds which were proven using this machinery.