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Article Dans Une Revue Journal of Knot Theory and Its Ramifications Année : 2013

G-links invariants, Markov traces and the semi-cyclic Uqsl2-modules

Résumé

Kashaev and Reshetikhin proposed a generalization of the Reshetikhin-Turaev link invariant construction to tangles with a flat connection in a principal G-bundle over the complement of the tangle. The purpose of this paper is to adapt and renormalize their construction to define invariants of G-links using the semi-cyclic representations of the non-restricted quantum group associated to sl2, defined by De Concini and Kac. Our construction uses a modified Markov trace. In our main example, the semi-cyclic invariants are a natural extension of the generalized Alexander polynomial invariants defined by Akutsu, Deguchi, and Ohtsuki. Surprisingly, direct computations suggest that these invariants are actually equal.

Dates et versions

hal-00866238 , version 1 (26-09-2013)

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Citer

Nathan Geer, Bertrand Patureau-Mirand. G-links invariants, Markov traces and the semi-cyclic Uqsl2-modules. Journal of Knot Theory and Its Ramifications, 2013, pp.Vol. 22, No. 11 (2013). ⟨10.1142/S0218216513500636⟩. ⟨hal-00866238⟩
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