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An invariant of links in a handlebody associated with the spin $ j$ representation of $ U\sb q(\mathfrak{sl}(2, \mathbf{C}))$

Author: Shigekazu Nakabo
Journal: Proc. Amer. Math. Soc. 118 (1993), 645-655
MSC: Primary 57M25; Secondary 17B37
MathSciNet review: 1132416
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Abstract: We construct an invariant of framed links in a handlebody by means of the spin $ j$ representation of $ {U_q}(\mathfrak{s}\mathfrak{l}(2,\mathbb{C}))$. We can see this invariant is an extension of the Jones polynomial and Kauffman's Dubrovnik polynomial. Moreover, we can obtain a linear representation of the generalized braid group associated with the Lie algebras of types $ B$ and $ C$ by applying the operators used in constructing an invariant to tangles in a solid torus.

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Keywords: Invariant of link, framed link, handlebody, spin $ j$ representation of $ {U_q}(\mathfrak{s}\mathfrak{l}(2,\mathbb{C}))$, Jones polynomial, Kauffman's Dubrovnik polynomial, generalized braid group
Article copyright: © Copyright 1993 American Mathematical Society

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