## Algebraic & Geometric Topology

### Closed surfaces and character varieties

Eric Chesebro

#### Abstract

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

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

Dates
Accepted: 3 March 2013
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715628

Digital Object Identifier
doi:10.2140/agt.2013.13.2001

Mathematical Reviews number (MathSciNet)
MR3073906

Zentralblatt MATH identifier
1270.57039

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

#### Citation

Chesebro, Eric. Closed surfaces and character varieties. Algebr. Geom. Topol. 13 (2013), no. 4, 2001--2037. doi:10.2140/agt.2013.13.2001. https://projecteuclid.org/euclid.agt/1513715628

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