2 problems

A composite knot is a nontrivial connected sum of knots, and a knot is persistently foliar if, for each boundary slope, its complement admits a co-oriented taut foliation meeting t…

Let $[K_1]$ and $[K_2]$ be isotopy classes of knots, and let $[K_1\sharp K_2]$ be their composite isotopy class. For an isotopy class $[K]$, write $E^{(2)}_{\circ}([K])$ for the in…