Generalized volume conjecture and the A-polynomials: The Neumann-Zagier potential function as a classical limit of the partition function

研究成果: ジャーナルへの寄稿学術誌査読

59 被引用数 (Scopus)

抄録

We introduce and study the partition function Zγ (M) for the cusped hyperbolic 3-manifold M. We construct formally this partition function based on an oriented ideal triangulation of M by assigning to each tetrahedron the quantum dilogarithm function, which is introduced by Faddeev in his studies of the modular double of the quantum group. Following Thurston and Neumann-Zagier, we deform a complete hyperbolic structure of M, and we define the partition function Zγ (Mu) correspondingly. This function is shown to give the Neumann-Zagier potential function in the classical limit γ → 0, and the A-polynomial can be derived from the potential function. We explain our construction by taking examples of 3-manifolds such as complements of hyperbolic knots and a punctured torus bundle over the circle.

本文言語英語
ページ(範囲)1895-1940
ページ数46
ジャーナルJournal of Geometry and Physics
57
9
DOI
出版ステータス出版済み - 8月 2007
外部発表はい

!!!All Science Journal Classification (ASJC) codes

  • 数理物理学
  • 物理学および天文学(全般)
  • 幾何学とトポロジー

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