Volume 5, issue 1 (2005)

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All roots of unity are detected by the A–polynomial

Eric Chesebro

Algebraic & Geometric Topology 5 (2005) 207–217
 arXiv: math.GT/0411205
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
Primary: 57M27
Secondary: 57M50