On \(\mathrm{SL}(3,\mathbb{C})\)-representations of the Whitehead link group

DOI10.1007/s10711-018-0404-8zbMath1506.57002arXiv1607.01536OpenAlexW2899988844MaRDI QIDQ2273262

Antonin Guilloux, Pierre Will

Publication date: 18 September 2019

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

Full work available at URL: https://arxiv.org/abs/1607.01536

zbMATH Keywords

geometric structureshyperbolic geometrycharacter varietiesrepresentations of fundamental groups of manifolds

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Algebraic moduli problems, moduli of vector bundles (14D20) Fundamental group, presentations, free differential calculus (57M05) Knot theory (57K10)

Related Items (6)

SL(3, ℂ)-character varieties of two-generator groups ⋮ Redundancy of Triangle Groups in Spherical CR Representations ⋮ Deformation Spaces of Discrete Groups of SU(2,1) in Quaternionic Hyperbolic Plane: A Case Study ⋮ Augmentations and link group representations ⋮ Spherical CR uniformization of Dehn surgeries of the Whitehead link complement ⋮ Dimension of representation and character varieties for two- and three-orbifolds

Uses Software

• SageMath
• SnapPy

Cites Work

• Unnamed Item
• Unnamed Item
• Geometry of the \(\mathrm{SL}(3,\mathbb{C})\)-character variety of torus knots
• Ptolemy coordinates, Dehn invariant and the \(A\)-polynomial
• Spherical CR Dehn surgeries
• Tetrahedra of flags, volume and homology of SL(3)
• Branched sperical CR structures on the complement of the figure-eight knot
• The complex volume of \(\mathrm{SL}(n,\mathbb{C})\)-representations of 3-manifolds
• A flag structure on a cusped hyperbolic 3-manifold
• A 1-parameter family of spherical CR uniformizations of the figure eight knot complement
• Varieties of group representations and splittings of 3-manifolds
• Dehn filling of the ``magic 3-manifold
• A spherical CR structure on the complement of the figure eight knot with discrete holonomy
• Valuations, trees, and degenerations of hyperbolic structures. I
• K-decompositions and 3d gauge theories
• Ideal triangle groups, dented tori, and numerical analysis.
• Complex hyperbolic geometry of the figure-eight knot
• Gluing equations for \(\mathrm{PGL}(n, \mathbb{C})\)-representations of 3-manifolds
• The \(SL(3,\mathbb{C})\)-character variety of the figure eight knot
• Generators, relations and symmetries in pairs of \(3\times 3\) unimodular matrices
• A complex hyperbolic Riley slice
• The SL(2, C) Casson Invariant for Knots and the Â-polynomial
• Character Varieties For : The Figure Eight Knot
• On Spherical CR Uniformization of 3-Manifolds
• Character varieties
• Two-generator groups acting on the complex hyperbolic plane
• Foundations of Hyperbolic Manifolds
• Spherical CR Geometry and Dehn Surgery (AM-165)
• Varieties of representations of finitely generated groups
• The structure of certain subgroups of the Picard group
• Deformation of hyperbolic manifolds in 𝑃𝐺𝐿(𝑛,𝐂) and discreteness of the peripheral representations
• Local Rigidity for -Representations of 3-Manifold Groups

This page was built for publication: On \(\mathrm{SL}(3,\mathbb{C})\)-representations of the Whitehead link group