Dehn surgery on arborescent links

This paper studies Dehn surgery on a large class of links, called arborescent links. It will be shown that if an arborescent link L is sufficiently complicated, in the sense that it is composed of at least 4 rational tangles T(p(i)/q(i)) with all q(i) > 2, and none of its length 2 tangles are of the form T(1/2(q1), 1/2(q2)), then all complete surgeries on L produce Haken manifolds. The proof needs some result on surgery on knots in tangle spaces. Let T(r/2s, p/2q) = (B, t(1) boolean OR t(2) boolean OR K) be a tangle with K a closed circle, and let M = B Int N(t(1) boolean OR t(2)). We will show that if s > 1 and p not equal +/-1 mod 2q, then partial derivative M remains incompressible after all nontrivial surgeries on K. Two bridge links are a subclass of arborescent links. For such a link L(p/q), most Dehn surgeries on it are non-Haken. However, it will be shown that all complete surgeries yield manifolds containing essential laminations, unless p/q has a partial fraction decomposition of the form 1/(r - 1/s), in which case it does admit non-laminar surgeries.