Taut foliations of torus knot complements

We show that for any torus knot K(r, s), vertical bar r vertical bar > s > 0, there is a family of taut foliations of the complement of K(r, s), which realizes all boundary slopes in (-infinity, 1) when r > 0, or (-1, infinity) when r < 0. This theorem is proved by a construction of branched surfaces and laminations which are used in the Roberts paper [5]. Applying this construction to a fibered knot K', we also show that there exists a family of taut foliations of the complement of the cable knot K of K' which realizes all boundary slopes in (-infinity, 1) or (-1, infinity). Further, we partially extend the theorem of Roberts to a link case.