Invariants of tangles with flat connections in their complements
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Let G be a simple complex algebraic group. By using a notion of a G-category we define invariants of tangles with flat G-connections in their complements. We also show that quantized universal enveloping algebras at roots of unity provide examples of G-categories.
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Cited by 3 Pith papers
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A quantization of the $\operatorname{SL}_2(\mathbb{C})$ Chern-Simons invariant of tangle exteriors
Defines invariants Z_N^ψ for tangles with flat sl_2 connections that recover a new description I^ψ of the SL_2(C) Chern-Simons invariant at N=1, built via unrestricted quantum sl_2 and holonomy R-matrices without phas...
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A quantization of the $\operatorname{SL}_2(\mathbb{C})$ Chern-Simons invariant of tangle exteriors
Constructs invariants Z_N^ψ of tangles with flat sl_2 connections using quantum sl_2 modules at roots of unity and holonomy R-matrices, recovering the SL_2(C) Chern-Simons invariant at N=1.
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The holonomy braiding for $\mathcal{U}_\xi(\mathfrak{sl}_2)$ in terms of geometric quantum dilogarithms
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.
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