DIFFERENCE AND DIFFERENTIAL EQUATIONS FOR THE COLORED JONES FUNCTION
نویسندگان
چکیده
منابع مشابه
Difference and Differential Equations for the Colored Jones Function
The colored Jones function of a knot is a sequence of Laurent polynomials. It was shown by TTQ. Le and the author that such sequences are q-holonomic, that is, they satisfy linear q-difference equations with coefficients Laurent polynomials in q and qn. We show from first principles that q-holonomic sequences give rise to modules over a q-Weyl ring. Frohman-Gelca-LoFaro have identified the latt...
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It can be conjectured that the colored Jones function of a knot can be computed in terms of counting paths on the graph of a planar projection of a knot. On the combinatorial level, the colored Jones function can be replaced by its weight system. We give two curious formulas for the weight system of a colored Jones function: one in terms of the permanent of a matrix associated to a chord diagra...
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The N-colored Jones polynomial JK (N) is one of the quantum invariants for knot K . It is associated with the N-dimensional irreducible representation of sl(2), and is powerful to classify knots. Motivated by “volume conjecture” [12, 18] saying that a hyperbolic volume of the knot complement dominates an asymptotic behavior of the colored Jones polynomial JK (N) at q = e2πi/N , it receives much...
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در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2008
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216508006245