Holonomy braidings, biquandles and quantum invariants of links with \(\mathsf{SL}_2(\mathbb{C})\) flat connections

DOI10.1007/s00029-020-0545-0zbMath1441.57010arXiv1806.02787OpenAlexW3010424081MaRDI QIDQ2310819

Bertrand Patureau-Mirand, Nicolai Reshetikhin, Nathan Geer, Christian Blanchet

Publication date: 6 April 2020

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.02787

zbMATH Keywords

quantum groupsknots and linksquandles

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Finite-type and quantum invariants, topological quantum field theories (TQFT) (57K16)

Related Items (7)

Holonomy invariants of links and nonabelian Reidemeister torsion ⋮ Non-semisimple extended topological quantum field theories ⋮ Vertex operator algebras and topologically twisted Chern-Simons-matter theories ⋮ Knot quandle decompositions ⋮ Twisted formalism for 3d \(\mathcal{N}=4\) theories ⋮ Quandle colorings vs. biquandle colorings ⋮ The trace on projective representations of quantum groups

Cites Work

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• Homology of left non-degenerate set-theoretic solutions to the Yang-Baxter equation
• The trace on projective representations of quantum groups
• Homotopy quantum field theory. With appendices by Michael Müger and Alexis Virelizier.
• A classifying invariant of knots, the knot quandle
• Spherical categories
• Some remarkable degenerations of quantum groups
• Renormalized Hennings invariants and \(2+1\)-TQFTs
• Biquandles and virtual links
• Traces on ideals in pivotal categories
• Hopf algebras with trace and representations
• Three-dimensional quantum gravity, Chern-Simons theory, and the \(A\)-polynomial
• G-LINKS INVARIANTS, MARKOV TRACES AND THE SEMI-CYCLIC U_q𝔰𝔩(2)-MODULES
• Quantum invariants of 3-manifolds via link surgery presentations and non-semi-simple categories
• Modified quantum dimensions and re-normalized link invariants
• DISTRIBUTIVE GROUPOIDS IN KNOT THEORY
• Quantum Coadjoint Action
• INVARIANTS OF COLORED LINKS
• REIDEMEISTER MOVES FOR SURFACE ISOTOPIES AND THEIR INTERPRETATION AS MOVES TO MOVIES
• Quandle cohomology and state-sum invariants of knotted curves and surfaces
• On 3-dimensional homotopy quantum field theory II: The surgery approach
• An algebraic condition to determine whether a knot is prime
• Invariants of tangles with flat connections in their complements
• Quantum invariants of knots and 3-manifolds

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