  Cohomological invariants of twisted wild character varieties as constructed
by Boalch and Yamakawa are derived from enumerative Calabi-Yau geometry and
refined Chern-Simons invariants of torus knots. Generalizing the untwisted
case, the present approach is based on a spectral correspondence for
meromorphic Higgs bundles with fixed conjugacy classes at the marked points.
This construction is carried out for twisted wild character varieties
associated to (l, kl-1) torus knots, providing a colored generalization of
existing results of Hausel, Mereb and Wong as well as Shende, Treumann and
Zaslow.
