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Holonomy braidings, biquandles and quantum invariants of links with $SL_2(\mathbb C)$ flat connections (1806.02787v1)
Published 7 Jun 2018 in math.GT and math.QA
Abstract: R. Kashaev and N. Reshetikhin introduced the notion of holonomy braiding extending V. Turaev's homotopy braiding to describe the behavior of cyclic representations of the unrestricted quantum group $U_qsl_2$ at root of unity. In this paper, using quandles and biquandles we develop a general theory for Reshetikhin-Turaev ribbon type functor for tangles with quandle representations. This theory applies to the unrestricted quantum group $U_qsl_2$ and produces an invariant of links with a gauge class of quandle representations.