ON THE COMPLEX VOLUME OF HYPERBOLIC KNOTS

DOI10.1142/S021821651100908XzbMath1226.57025arXivmath/0009165MaRDI QIDQ5198410

Yoshiyuki Yokota

Publication date: 8 August 2011

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0009165

zbMATH Keywords

hyperbolic knotvolume conjectureChern-Simons invariantcomplex volume

Mathematics Subject Classification ID

General geometric structures on low-dimensional manifolds (57M50)

Related Items (22)

Modularity and value distribution of quantum invariants of hyperbolic knots ⋮ Octahedral developing of knot complement. I: Pseudo-hyperbolic structure ⋮ The universal quantum invariant and colored ideal triangulations ⋮ The complex volumes of twist knots ⋮ Optimistic limits of Kashaev invariants and complex volumes of hyperbolic links ⋮ A characterization of alternating link exteriors in terms of cubed complexes ⋮ On the asymptotic expansions of the Kashaev invariant of the knots with 6 crossings ⋮ Reidemeister transformations of the potential function and the solution ⋮ Symplectic quandles and parabolic representations of 2-bridge knots and links ⋮ An application of non-positively curved cubings of alternating links ⋮ Braids, complex volume and cluster algebras ⋮ Noncompact Fuchsian and quasi-Fuchsian surfaces in hyperbolic 3-manifolds ⋮ Representations of the quantum Teichmüller space and invariants of surface diffeomorphisms ⋮ Quandle theory and the optimistic limits of the representations of link groups ⋮ The reduced Dijkgraaf–Witten invariant of double twist knots in the Bloch group of 𝔽p ⋮ Optimistic limit of the colored Jones polynomial and the existence of a solution ⋮ On the cusp shape of hyperbolic knots ⋮ OPTIMISTIC LIMITS OF THE COLORED JONES POLYNOMIALS AND THE COMPLEX VOLUMES OF HYPERBOLIC LINKS ⋮ Kashaev's Conjecture and the Chern-Simons Invariants of Knots and Links ⋮ The reduced Dijkgraaf–Witten invariant of twist knots in the Bloch group of a finite field ⋮ The colored Jones polynomials as vortex partition functions ⋮ On the Kashaev invariant and the twisted Reidemeister torsion of two-bridge knots

Cites Work

• The hyperbolic volume of knots from the quantum dilogarithm
• The volume and Chern-Simons invariant of a representation
• Volumes of hyperbolic three-manifolds
• Extended Bloch group and the Cheeger-Chern-Simons class
• The complex volumes of twist knots
• The colored Jones polynomials and the simplicial volume of a knot

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