Weights of essential surfaces in 2-bridge knot complements

Cynthia L. Curtis; Kendra Ebke; Kate O'Connor

doi:10.1016/j.topol.2026.109848

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arXiv · 2605.21639

Weights of essential surfaces in 2-bridge knot complements

Cynthia L. Curtis·Kendra Ebke·Kate O'Connor

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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 $K$, 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.

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Cynthia L. Curtis, Kendra Ebke, Kate O'Connor. 2026-05-20. Weights of essential surfaces in 2-bridge knot complements. https://doi.org/10.1016/j.topol.2026.109848

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