Journal für die reine und angewandte Mathematik (Crelles Journal)

Issue: Jun 2007

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Issue: Jun 2007

Volume 2007, Number 607

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The colored Jones polynomials of the figure-eight knot and its Dehn surgery spaces

Hitoshi Murakami¹,

¹Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan.

Yoshiyuki Yokota²

²Department of Mathematics, Tokyo Metropolitan University, Tokyo 192-0397, Japan.

Citation Information. Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2007, Issue 607, Pages 47–68, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2007.045, June 2007

Publication History: Received: 12/12/2005; revised: 06/03/2006; published online: 22/07/2007

Abstract

We calculate limits of the colored Jones polynomials of the figure-eight knot and conclude that in most cases they determine the volumes and the Chern-Simons invariants of the three-manifolds obtained by Dehn surgeries along it.

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