  We introduce and explore the relation between quivers and 3-manifolds with
the topology of the knot complement. This idea can be viewed as an adaptation
of the knots-quivers correspondence to Gukov-Manolescu invariants of knot
complements (also known as $F_K$ or $\hat{Z}$). Apart from assigning quivers to
complements of $T^{(2,2p+1)}$ torus knots, we study the physical interpretation
in terms of the BPS spectrum and general structure of 3d $\mathcal{N}=2$
theories associated to both sides of the correspondence. We also make a step
towards categorification by proposing a $t$-deformation of all objects
mentioned above.
