Geometric triangulations and the Teichmüller TQFT volume conjecture for twist knots

DOI10.4171/qt/178arXiv1903.09480OpenAlexW3036227902WikidataQ123227059 ScholiaQ123227059MaRDI QIDQ6062673

Francçois Guéritaud, Fathi Ben Aribi, Eiichi Piguet-Nakazawa

Publication date: 6 November 2023

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

Full work available at URL: https://arxiv.org/abs/1903.09480

zbMATH Keywords

3-manifoldstriangulationssaddle point methodhyperbolic volumevolume conjecturequantum topologytwist knotsTeichmüller TQFT

Mathematics Subject Classification ID

Triangulating (57R05) Finite-type and quantum invariants, topological quantum field theories (TQFT) (57K16) Knot theory (57K10) Hyperbolic 3-manifolds (57K32)

Cites Work

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• A TQFT of Turaev-Viro type on shaped triangulations
• Construction of spines of two-bridge link complements and upper bounds of their Matveev complexities
• Topological quantum field theories
• The hyperbolic volume of knots from the quantum dilogarithm
• On canonical triangulations of once-punctured torus bundles and two-bridge link complements. With an appendix by David Futer.
• Volumes of hyperbolic three-manifolds
• Three-manifold invariants derived from the Kauffman bracket
• State sum invariants of 3-manifolds and quantum \(6j\)-symbols
• Teichmüller TQFT vs. Chern-Simons theory
• Volume conjectures for the Reshetikhin-Turaev and the Turaev-Viro invariants
• On the asymptotic expansion of the quantum SU(2) invariant at \(q =exp(4{\pi}\sqrt{-1}/N\)) for closed hyperbolic 3-manifolds obtained by integral surgery along the figure-eight knot
• Ribbon graphs and their invariants derived from quantum groups
• Quantum hyperbolic invariants of 3-manifolds with PSL\((2,\mathbb C)\)-characters
• Topological quantum field theories derived from the Kauffman bracket
• The quantum content of the gluing equations
• Invariants of 3-manifolds via link polynomials and quantum groups
• Proof of the volume conjecture for Whitehead chains
• The Teichmüller TQFT volume conjecture for twist knots
• A sound and complete proof theory for propositional logical contingencies
• A TQFT from quantum Teichmüller theory
• Strong rigidity of Q-rank 1 lattices
• QUANTUM DILOGARITHM AS A 6j-SYMBOL
• Polyhedra representation of link complements
• An Introduction to the Volume Conjecture
• From angled triangulations to hyperbolic structures
• Volume Conjecture for Knots
• The complex volumes of twist knots
• The Dilogarithm Function
• COMPLEXITY OF LINKS IN 3-MANIFOLDS
• A polynomial invariant for knots via von Neumann algebras
• Three dimensional manifolds, Kleinian groups and hyperbolic geometry
• Combinatorics of the Teichmüller TQFT
• Asymptotic aspects of the Teichm\"uller TQFT
• Coloured Jones invariants of links and the Volume Conjecture
• ASYMPTOTICS OF THE QUANTUM INVARIANTS FOR SURGERIES ON THE FIGURE 8 KNOT
• Strong Rigidity of Locally Symmetric Spaces. (AM-78)
• The colored Jones polynomials and the simplicial volume of a knot

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