#### Algebraic and Geometric Topology 5 (2005),
paper no. 11, pages 207-217.

## All roots of unity are detected by the A-polynomial

### Eric Chesebro

**Abstract**. For an arbitrary positive integer n, we
construct infinitely many one-cusped hyperbolic 3-manifolds where each
manifold's A-polynomial detects every n-th root of unity. This answers
a question of Cooper, Culler, Gillet, Long, and Shalen as to which
roots of unity arise in this manner.
**Keywords**.
Character variety, ideal point, A-polynomial

**AMS subject classification**.
Primary: 57M27.
Secondary: 57M50.

**DOI:** 10.2140/agt.2005.5.207

**E-print:** `arXiv:math.GT/0411205`

Submitted: 23 February 2005.
Accepted: 6 March 2005.
Published: 28 March 2005.

Notes on file formats
Eric Chesebro

Department of Mathematics, The University of Texas at Austin

Austin, TX 78712-0257, USA

Email: chesebro@math.utexas.edu

URL: http://www.ma.utexas.edu/users/chesebro/

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