Dehn surgery on arborescent knots and links—A survey

Abstract

In this survey, we present some recent results about Dehn surgeries on arborescent knots and links. Arborescent links are also known as algebraic links [1, 2] and star links [3]. The set of arborescent knots and links is a large class, including all 2-bridge links and Montesinos links. They have been studied by many people, see e.g. [4,2,5,3,6, 7]. We will give some definitions below. The reader is referred to [8, 9] for more detailed background material for 3-manifold topology, to [2,1,4,10] for arborescent tangles and links, to [11] for hyperbolic manifolds, and to [12] for essential laminations and branched surfaces.