Quantum hyperbolic geometry

DOI10.2140/agt.2007.7.845zbMath1139.57008arXivmath/0611504OpenAlexW3099763305MaRDI QIDQ2464776

Stéphane Baseilhac, Riccardo Benedetti

Publication date: 17 December 2007

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0611504

zbMATH Keywords

quantum field theoryhyperbolic geometryquantum invariantsmapping class group representationsCheeger-Chern-Simons classdilogarithms

Mathematics Subject Classification ID

Related Items (15)

A TQFT of Turaev-Viro type on shaped triangulations ⋮ The universal quantum invariant and colored ideal triangulations ⋮ Notes on a paper of Mess ⋮ Classical and quantum dilogarithmic invariants of flat \(\text{PSL}(2,\mathbb C)\)-bundles over 3-manifolds ⋮ Optimistic limits of Kashaev invariants and complex volumes of hyperbolic links ⋮ Topological invariants from nonrestricted quantum groups ⋮ 1-efficient triangulations and the index of a cusped hyperbolic 3-manifold ⋮ Tangle functors from semicyclic representations ⋮ Unicity for representations of the Kauffman bracket skein algebra ⋮ Analytic families of quantum hyperbolic invariants ⋮ Representations of the quantum Teichmüller space and invariants of surface diffeomorphisms ⋮ \(6j\)-symbols, hyperbolic structures and the volume conjecture ⋮ Quandle theory and the optimistic limits of the representations of link groups ⋮ A TQFT from quantum Teichmüller theory ⋮ Generic flows on 3-manifolds

Cites Work

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• Topological quantum field theories
• The hyperbolic volume of knots from the quantum dilogarithm
• A dilogarithmic formula for the Cheeger-Chern-Simons class
• The decorated Teichmüller space of punctured surfaces
• The real analytic theory of Teichmüller space
• Incompressible surfaces in punctured-torus bundles
• Lectures on hyperbolic geometry
• State sum invariants of 3-manifolds and quantum \(6j\)-symbols
• On the character variety of group representations in \(\text{SL}(2,\mathbb{C})\) and \(\text{PSL}(2,\mathbb{C})\)
• Shearing hyperbolic surfaces, bending pleated surfaces and Thurston's symplectic form
• The canonical decomposition of once-punctured torus bundles
• Algebraic and geometric solutions of hyperbolicity equations
• Coordinates for the moduli space of flat PSL\((2,\mathbb{R})\)-connections
• The Weil-Petersson and Thurston symplectic forms
• Extended Bloch group and the Cheeger-Chern-Simons class
• Positively oriented ideal triangulations on hyperbolic three-manifolds
• Quantum hyperbolic invariants of 3-manifolds with PSL\((2,\mathbb C)\)-characters
• Negatively oriented ideal triangulations and a proof of Thurston's hyperbolic Dehn filling theorem
• Classical and quantum dilogarithmic invariants of flat \(\text{PSL}(2,\mathbb C)\)-bundles over 3-manifolds
• Representations of the quantum Teichmüller space and invariants of surface diffeomorphisms
• The variety of characters in \(\text{PSL}_2(\mathbb{C})\)
• NONABELIAN REPRESENTATIONS OF 2-BRIDGE KNOT GROUPS
• Canonical Wick rotations in 3-dimensional gravity
• Quantum invariants of knots and 3-manifolds

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