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.

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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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