منابع مشابه
The Quantum G2 Link Invariant
We derive an inductive, combinatorial definition of a polynomial-valued regular isotopy invariant of links and tangled graphs. We show that the invariant equals the Reshetikhin-Turaev invariant corresponding to the exceptional simple Lie algebra G2. It is therefore related to G2 in the same way that the HOMFLY polynomial is related to An and the Kauffman polynomial is related to Bn, Cn, and Dn....
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We consider an asymptotic expansion of Kashaev’s invariant or of the colored Jones function for the torus link T (2, 2m). We shall give q-series identity related to these invariants, and show that the invariant is regarded as a limit of q being N -th root of unity of the Eichler integral of a modular form of weight 3/2 which is related to the ŝu(2)m−2 character.
متن کاملQuantum Knot Invariant for Torus Link and Modular Forms
Recent studies reveal an intimate connection between the quantum knot invariant and the “nearly modular form” especially with the half integral weight. In Ref. 8 Lawrence and Zagier studied an asymptotic expansion of the Witten–Reshetikhin–Turaev invariant of the Poincaré homology sphere, and they showed that the invariant can be regarded as the Eichler integral of the modular form of weight 3/...
متن کاملMATRIX FACTORIZATIONS AND DOUBLE LINE IN sln QUANTUM LINK INVARIANT
L. Kauffman introduced a graphical link invariant which is the normalized Jones polynomial [4][5]. It is well-known that the polynomial is derived from the fundamental representation of the quantum group Uq(sl2). Further, G. Kuperberg constructed a graphical link invariant associated with the fundamental representation of the quantum group Uq(sl3) [10]. H. Murakami, T. Ohtsuki and S. Yamada int...
متن کاملLink invariant of the Izergin–Korepin model
The link invariant associated with the Izergin–Korepin 19-vertex model is deduced using the method of statistical mechanics. It is shown that the Izergin–Korepin model leads to an invariant which is precisely the 3-state Akutsu–Wadati polynomial, previously known only for 2and 3-braid knots. We give a table of the invariant for all knots and links up to seven crossings.
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ژورنال
عنوان ژورنال: International Journal of Mathematics
سال: 1994
ISSN: 0129-167X,1793-6519
DOI: 10.1142/s0129167x94000048