Edges of canonical decompositions for 2-bridge knots and links (Q1282310)

Let \(L=C(a_1, \dots , a_k)\) be a hyperbolic 2-bridge knot or link. The authors describe a family of arcs in \(S^3-L\) which are ambient isotopic to edges of the canonical decomposition of \(S^3-L\) if each \(|a_j|\) is sufficiently large. The result supports the following conjecture due to Sakuma and Weeks: Every unknotting tunnel for a cusped hyperbolic three-manifold is isotopic to an edge of the canonical decomposition.