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Detecting essential surfaces as intersections in the character variety

Michelle Chu

Algebraic & Geometric Topology 17 (2017) 2893–2914

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 nonintegral and detect a Seifert surface.

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character variety, two-bridge knots, essential surfaces
Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 20C15, 57M27, 57M50
Received: 21 September 2016
Revised: 14 April 2017
Accepted: 12 June 2017
Published: 19 September 2017
Michelle Chu
Department of Mathematics
The University of Texas
Austin, TX
United States