Braids, complex volume and cluster algebras

DOI10.2140/agt.2015.15.2175zbMath1351.57009arXiv1304.4776OpenAlexW3102650535MaRDI QIDQ498732

Kazuhiro Hikami, Rei Inoue

Publication date: 29 September 2015

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

Full work available at URL: https://arxiv.org/abs/1304.4776

zbMATH Keywords

knothyperbolic volumecluster algebracomplex volume

Mathematics Subject Classification ID

Related Items (11)

Check-operators and quantum spectral curves ⋮ Octahedral developing of knot complement. I: Pseudo-hyperbolic structure ⋮ The universal quantum invariant and colored ideal triangulations ⋮ Quandle theory and the optimistic limits of the representations of link groups ⋮ On the Hikami-Inoue conjecture ⋮ On groups Gnk and Γnk: A study of manifolds, dynamics, and invariants ⋮ Cluster realizations of Weyl groups and higher Teichmüller theory ⋮ Solution of tetrahedron equation and cluster algebras ⋮ OPTIMISTIC LIMITS OF THE COLORED JONES POLYNOMIALS AND THE COMPLEX VOLUMES OF HYPERBOLIC LINKS ⋮ Artin’s braids, braids for three space, and groups Γn4 and Gnk ⋮ Cluster algebras and Jones polynomials

Cites Work

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• The hyperbolic volume of knots from the quantum dilogarithm
• Quandle homology and complex volume
• The volume and Chern-Simons invariant of a representation
• Cluster algebras and triangulated surfaces. I: Cluster complexes
• Proof of the volume conjecture for torus knots
• Torus knot and minimal model
• Extended Bloch group and the Cheeger-Chern-Simons class
• A LINK INVARIANT FROM QUANTUM DILOGARITHM
• HYPERBOLIC STRUCTURE ARISING FROM A KNOT INVARIANT
• Cluster algebras I: Foundations
• Optimistic limits of Kashaev invariants and complex volumes of hyperbolic links
• Braiding operator via quantum cluster algebra
• THE COMPLEX VOLUMES OF TWIST KNOTS VIA COLORED JONES POLYNOMIALS
• The complex volumes of twist knots
• Cluster algebras IV: Coefficients
• On a Yang-Baxter map and the Dehornoy ordering
• Cluster Ensembles, Quantization and the Dilogarithm II: The Intertwiner
• ON THE COMPLEX VOLUME OF HYPERBOLIC KNOTS
• CLUSTER ALGEBRA AND COMPLEX VOLUME OF ONCE-PUNCTURED TORUS BUNDLES AND 2-BRIDGE LINKS
• Periodicities in cluster algebras and dilogarithm identities
• The colored Jones polynomials and the simplicial volume of a knot
• Vassiliev invariants and a strange identity related to the Dedekind eta-function

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