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Squeezed knots are those knots that appear as slices of genus-minimizing oriented smooth cobordisms between positive and negative torus knots. We show that this class of knots is large and discuss how to obstruct squeezedness. The most effective obstructions appear to come from quantum knot invariants, notably including refinements of the Rasmussen invariant due to Lipshitz–Sarkar and Sarkar–Scaduto–Stoffregen involving stable cohomology operations on Khovanov homology.
Feller et al. (Fri,) studied this question.