Culler-Shalen seminorms of fillings of the Whitehead link exterior

Abstract

We determine the total Culler-Shalen seminorms for the 3-manifolds W_{p/q}:=W(p/q,-) obtained by Dehn filling with slope p/q on one boundary component of the Whitehead link exterior W when p is odd. As part of the proof, we use an explicit parametrization of the eigenvalue variety of W to find a one-variable polynomial whose roots characterize characters of p-reps of \pi_{1}(W_{p/q}), i.e. representations with values in SL_2(C) which are parabolic on the peripheral subgroup.