Algebraic & Geometric Topology

Closed surfaces and character varieties

Eric Chesebro

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The powerful character variety techniques of Culler and Shalen can be used to find essential surfaces in knot manifolds. We show that module structures on the coordinate ring of the character variety can be used to identify detected boundary slopes as well as when closed surfaces are detected. This approach also yields new number theoretic invariants for the character varieties of knot manifolds.

Article information

Algebr. Geom. Topol., Volume 13, Number 4 (2013), 2001-2037.

Received: 22 February 2013
Accepted: 3 March 2013
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds

3–manifold character variety essential surface


Chesebro, Eric. Closed surfaces and character varieties. Algebr. Geom. Topol. 13 (2013), no. 4, 2001--2037. doi:10.2140/agt.2013.13.2001.

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