  There are several knot invariants in the literature that are defined using
singular instantons. Such invariants provide strong tools to study the knot
group and give topological applications. For instance, it gives powerful tools
to study the topology of knots in terms of representations of fundamental
groups. In particular, it is shown that any traceless representation of the
torus knot group can be extended to any concordance from the torus knot to
another knot. Daemi and Scaduto proposed a generalization that is related to a
version of the Slice-Ribbon conjecture to torus knots. The results of this
paper provide further evidence towards the positive answer to this question.
The method is a generalization of Daemi-Scaduto's equivariant singular
instanton Floer theory following Echeverria's earlier work. Moreover, the
irreducible singular instanton homology of torus knots for all but finitely
many rational holonomy parameters are determined as $\mathbb{Z}/4$-graded
abelian groups.
