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arxiv: 1806.02787 · v1 · pith:PGTJSM4Znew · submitted 2018-06-07 · 🧮 math.GT · math.QA

Holonomy braidings, biquandles and quantum invariants of links with SL₂(mathbb C) flat connections

Christian Blanchet , Nathan Geer , Bertrand Patureau-Mirand , Nicolai Reshetikhin This is my paper
classification 🧮 math.GT math.QA
keywords quantumrepresentationsbiquandlesbraidinggroupholonomylinksquandle
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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.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. The holonomy braiding for $\mathcal{U}_\xi(\mathfrak{sl}_2)$ in terms of geometric quantum dilogarithms

    math.QA 2025-09 unverdicted novelty 5.0

    Derives explicit factorization of the holonomy R-matrix for U_ξ(sl₂) at a root of unity into four geometric quantum dilogarithms satisfying a holonomy Yang-Baxter equation.