The contact annulus twist–Luttinger surgery conjecture for Stein traces

Let a Stein trace be the Stein $4$-manifold obtained from a Legendrian knot by attaching a Stein $2$-handle. Contact annulus twists modify the knot and its contact data, while Luttinger surgeries are the corresponding symplectic torus surgeries. Contact annulus twist–Luttinger surgery conjecture. The analogue of the theorem relating annulus twists and torus surgeries holds for contact annulus twists and Luttinger surgeries of Stein traces. The paper presents this as a direction for future work; no resolution is supplied in the text.