Weights of essential surfaces in 2-bridge knot complements
Geometric Topology
2026-05-22 v1
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.
Keywords
Cite
@article{arxiv.2605.21639,
title = {Weights of essential surfaces in 2-bridge knot complements},
author = {Cynthia L. Curtis and Kendra Ebke and Kate O'Connor},
journal= {arXiv preprint arXiv:2605.21639},
year = {2026}
}
Comments
Near final version. Final article in press:Topology and its Applications 387 (2026), article 109848