Quantized representations of knot groups

DOI10.4171/qt/191arXiv1812.09539OpenAlexW4388279393MaRDI QIDQ6190472

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Publication date: 6 February 2024

Published in: Quantum Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.09539

zbMATH Keywords

Hopf algebrasknotsquantum groupslinksrepresentation varietiesbraided groups

Mathematics Subject Classification ID

Quantum groups (quantized function algebras) and their representations (20G42) Hopf algebras and their applications (16T05) Knot theory (57K10)

Cites Work

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• The hyperbolic volume of knots from the quantum dilogarithm
• The colored Jones polynomial and the \(A\)-polynomial of knots
• Solutions of the braid equation related to a Hopf algebra
• Quantum character varieties and braided module categories
• Volume conjectures for the Reshetikhin-Turaev and the Turaev-Viro invariants
• Braided groups
• Quantum Riemann surfaces in Chern-Simons theory
• Cohomology of the adjoint of Hopf algebras.
• The finiteness conjecture for skein modules
• Quantized trace rings
• Examples of braided groups and braided matrices
• Quantum and braided linear algebra
• 𝑆𝐿(2) Representations of Finitely Presented Groups
• The colored Jones polynomials and the simplicial volume of a knot

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