Detecting essential surfaces as intersections in the character variety

Chu, Michelle

doi:10.2140/agt.2017.17.2893

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Detecting essential surfaces as intersections in the character variety

Michelle Chu

Algebraic & Geometric Topology 17 (2017) 2893–2914

DOI: 10.2140/agt.2017.17.2893

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 nonintegral and detect a Seifert surface.

Keywords

character variety, two-bridge knots, essential surfaces

Mathematical Subject Classification 2010

Primary: 57M25

Secondary: 20C15, 57M27, 57M50

References

Publication

Received: 21 September 2016

Revised: 14 April 2017

Accepted: 12 June 2017

Published: 19 September 2017

Authors

Michelle Chu
Department of Mathematics The University of Texas Austin, TX United States

Volume 17, issue 5 (2017)