CLUSTER ALGEBRA AND COMPLEX VOLUME OF ONCE-PUNCTURED TORUS BUNDLES AND 2-BRIDGE LINKS

DOI10.1142/S0218216514500060zbMath1314.57005arXiv1212.6042OpenAlexW2017305048MaRDI QIDQ5410993

Rei Inoue, Kazuhiro Hikami

Publication date: 17 April 2014

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

Full work available at URL: https://arxiv.org/abs/1212.6042

zbMATH Keywords

hyperbolic geometryknot complementcluster algebracomplex volume

Mathematics Subject Classification ID

Cluster algebras (13F60)

Related Items

Check-operators and quantum spectral curves, \(\mathrm{SU}(2)/\mathrm{SL}(2)\) knot invariants and Kontsevich-Soibelman monodromies, Note on character varieties and cluster algebras, Braids, complex volume and cluster algebras, On the Hikami-Inoue conjecture

Uses Software

• SnapPy

Cites Work

• Unnamed Item
• 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.
• Punctured torus groups and 2-bridge knot groups. I
• The volume and Chern-Simons invariant of a representation
• Generalized volume conjecture and the \(A\)-polynomials: The Neumann-Zagier potential function as a classical limit of the partition function
• Cluster algebras and triangulated surfaces. I: Cluster complexes
• Exact results for perturbative Chern-Simons theory with complex gauge group
• Volumes of hyperbolic three-manifolds
• Incompressible surfaces in punctured-torus bundles
• Extended Bloch group and the Cheeger-Chern-Simons class
• Moduli spaces of local systems and higher Teichmüller theory
• Cluster algebras I: Foundations
• Cluster algebras IV: Coefficients
• The colored Jones polynomials and the simplicial volume of a knot