All roots of unity are detected by the A–polynomial

Chesebro, Eric

doi:10.2140/agt.2005.5.207

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All roots of unity are detected by the A–polynomial

Eric Chesebro

Algebraic & Geometric Topology 5 (2005) 207–217

DOI: 10.2140/agt.2005.5.207

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

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/

Volume 5, issue 1 (2005)