Weights of essential surfaces in 2-bridge knot complements
arXiv:2605.21639 · doi:10.1016/j.topol.2026.109848
Abstract
Understanding ideal points in the character varieties of knot complements has led to a number of important invariants for 3-manifolds. Ohtsuki (1994) counted the ideal points for character varieties of 2-bridge knot complements, and he made his techniques more concrete in an ensuing paper (1996). Drawing on these ideas, for all 2-bridge knots , we explicitly determine the structure of a Serre tree for each essential surface in the knot complement directly from the knot diagram. Using these trees, we derive a formula for the number of ideal points associated to each incompressible surface.
Near final version. Final article in press:Topology and its Applications 387 (2026), article 109848