کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1896977 | 1044472 | 2007 | 46 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Generalized volume conjecture and the A-polynomials: The Neumann-Zagier potential function as a classical limit of the partition function
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
فیزیک ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
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 γâ0, 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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Geometry and Physics - Volume 57, Issue 9, August 2007, Pages 1895-1940
Journal: Journal of Geometry and Physics - Volume 57, Issue 9, August 2007, Pages 1895-1940
نویسندگان
Kazuhiro Hikami,