Quantum invariants of links and 3-valent graphs in 3-manifolds

DOI10.1007/BF02699190zbMath0822.57012MaRDI QIDQ1314736

Vladimir G. Turaev

Publication date: 17 October 1995

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=PMIHES_1993__77__121_0

zbMATH Keywords

compact 3-manifoldJones polynomialquantum invariantsTuraev-Viro invariantsquantum \(6j\)-symbolembedded 3-valent fat graphSU(2) quantum invariants

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)

Related Items (9)

Topological quantum field theory and invariants of graphs for quantum groups ⋮ On Kauffmann invariants for 6-valent graphs ⋮ Microscopic description of 2D topological phases, duality, and 3D state sums ⋮ Turaev–Viro invariant and 3nj symbols ⋮ Invariants of Three-Manifolds, Unitary Representations of the Mapping Class Group, and Numerical Calculations ⋮ Geometrical measurements in three-dimensional quantum gravity ⋮ Invariants of SPIN networks embedded in three-manifolds ⋮ Unnamed Item ⋮ On the relation between two quantum group invariants of 3-cobordisms

Cites Work

• Topological quantum field theories
• State models and the Jones polynomial
• The Yang-Baxter equation and invariants of links
• Quantum field theory and the Jones polynomial
• Shadow links and face models of statistical mechanics
• State sum invariants of 3-manifolds and quantum \(6j\)-symbols
• Ribbon graphs and their invariants derived from quantum groups
• Invariants of 3-manifolds via link polynomials and quantum groups
• A polynomial invariant for knots via von Neumann algebras
• TRANSFORMATIONS OF SPECIAL SPINES AND THE ZEEMAN CONJECTURE
• A Set of Orthogonal Polynomials That Generalize the Racah Coefficients or $6 - j$ Symbols
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