For all 2-bridge knots, Serre trees of essential surfaces are read off the diagram to produce a formula counting associated ideal points in the character variety.
Ohutsuki,How to construct ideal points ofSL 2(C)representation spaces of knot groups,Topology App.93(2) (1999), 131–159
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Weights of essential surfaces in 2-bridge knot complements
For all 2-bridge knots, Serre trees of essential surfaces are read off the diagram to produce a formula counting associated ideal points in the character variety.