The volume conjecture for polyhedra implies the Stoker conjecture

DOI10.1007/s10711-023-00813-yzbMath1528.57022arXiv2209.13439OpenAlexW4382284113MaRDI QIDQ6112060

Giulio Belletti

Publication date: 7 July 2023

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.13439

zbMATH Keywords

hyperbolic polyhedravolume conjectureStoker conjecture

Mathematics Subject Classification ID

Three-dimensional polytopes (52B10) Length, area, volume and convex sets (aspects of convex geometry) (52A38) PL-topology (57Q99) Finite-type and quantum invariants, topological quantum field theories (TQFT) (57K16)

Cites Work

• Unnamed Item
• Unnamed Item
• Deformations of hyperbolic convex polyhedra and cone-3-manifolds
• On the asymptotic expansion of the Kashaev invariant of the \(5_2\) knot
• The hyperbolic volume of knots from the quantum dilogarithm
• On the volume conjecture for polyhedra
• Quantum field theory and the Jones polynomial
• A characterization of compact convex polyhedra in hyperbolic 3-space
• 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
• A characterization of ideal polyhedra in hyperbolic 3-space
• Topological invariants of graphs in 3-space
• The deformation theory of hyperbolic cone-3-manifolds with cone-angles less than \(2\pi\)
• Complex twist flows on surface group representations and the local shape of the deformation space of hyperbolic cone-3-manifolds
• Growth of quantum \(6j\)-symbols and applications to the volume conjecture
• \(6j\)-symbols, hyperbolic structures and the volume conjecture
• The uniquely embeddable planar graphs
• Hyperideal polyhedra in hyperbolic 3-space
• On the asymptotic expansions of the Kashaev invariant of the knots with 6 crossings
• On the asymptotic expansions of the Kashaev invariant of hyperbolic knots with seven crossings
• Combinatorial Decompositions, Kirillov–Reshetikhin Invariants, and the Volume Conjecture for Hyperbolic Polyhedra
• The maximum volume of hyperbolic polyhedra
• Geometrical problems concerning polyhedra in the large
• The colored Jones polynomials and the simplicial volume of a knot
• Asymptotics of quantum \(6j\) symbols