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arXiv · 1303.4935

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

Nathan Geer·Bertrand Patureau-Mirand
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Abstract

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.

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BibTeXRIS

Nathan Geer, Bertrand Patureau-Mirand. 2013-03-20. G-links invariants, Markov traces and the semi-cyclic Uqsl2-modules. https://arxiv.org/abs/1303.4935

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