Volume 5, issue 1 (2005)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 nth 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
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57M50
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Publication
Received: 23 February 2005
Accepted: 6 March 2005
Published: 28 March 2005
Authors
Eric Chesebro
Department of Mathematics
The University of Texas at Austin
Austin TX 78712-0257
USA
http://www.ma.utexas.edu/users/chesebro/