The L-space conjecture for persistently foliar knots

A knot $\kappa$ in $S^3$ is an L-space knot if some non-trivial Dehn surgery on $\kappa$ yields an L-space, and it is persistently foliar if, for each boundary slope, its complement admits a co-oriented taut foliation meeting the boundary transversely in curves of that slope. L-space knot conjecture. A knot is persistently foliar if and only if it is not an L-space knot and has no reducible surgeries. This relates taut foliations and L-spaces to Dehn surgery on knots; the source does not give evidence of resolution.