Detecting essential surfaces as intersections in the character variety

Abstract

We describe a family of hyperbolic knots whose character variety contain exactly two distinct components of characters of irreducible representations. The intersection points between the components carry rich topological information. In particular, these points are non-integral and detect the Seifert surface.

v2: 17 pages, 4 figures. Corrected an error and added Lemma 4.4

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