  We apply and illustrate the techniques of spectral networks in a large
collection of A_{K-1} theories of class S, which we call "lifted A_1 theories."
Our construction makes contact with Fock and Goncharov's work on higher
Teichmuller theory. In particular we show that the Darboux coordinates on
moduli spaces of flat connections which come from certain special spectral
networks coincide with the Fock-Goncharov coordinates. We show, moreover, how
these techniques can be used to study the BPS spectra of lifted A_1 theories.
In particular, we determine the spectrum generators for all the lifts of a
simple superconformal field theory.
