  We study the relationship between Ng's abelian cord ring and SL(2,C)
characters of the two-fold branched cover $\Sigma(K)$. Augmentations, and their
corresponding rank, play a central role in the relationship. Our study also
leads to a correspondence between trace-free SL(2,C) characters of a knot
complement and augmentations. Whether the trace-free character is metabelian or
not is determined by the rank of the corresponding augmentation. Necessary and
sufficient conditions are given on the augmentation for it to correspond to an
SU(2) character. This provides an effective tool for finding representations of
relevance to singular instanton homology. We also give necessary and sufficient
conditions for an augmentation to induce a non-abelian SL(2,R) character of
$\Sigma(K)$ and exploit this to discuss branched covers with left-orderable
fundamental group.
