Representations of fundamental groups of 3-manifolds into \(\mathrm{PGL}(3,\mathbb C)\): exact computations in low complexity

DOI10.1007/s10711-014-9987-xzbMath1326.57041arXiv1307.6697OpenAlexW2312683364MaRDI QIDQ2516428

Elisha Falbel, Fabrice Rouillier, Pierre-Vincent Koseleff

Publication date: 3 August 2015

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

Full work available at URL: https://arxiv.org/abs/1307.6697

zbMATH Keywords

3-manifoldsrepresentationsCR structuresflag structures\(\mathbb C\))0-dimensional variety solvingPGL(3

Mathematics Subject Classification ID

Related Items (19)

Ptolemy coordinates, Dehn invariant and the \(A\)-polynomial ⋮ SL(3, ℂ)-character varieties of two-generator groups ⋮ Triangulation independent Ptolemy varieties ⋮ A complex hyperbolic Riley slice ⋮ Redundancy of Triangle Groups in Spherical CR Representations ⋮ A uniformizable spherical CR structure on a two-cusped hyperbolic 3-manifold ⋮ Dimension of character varieties for $3$-manifolds ⋮ Tetrahedra of flags, volume and homology of SL(3) ⋮ Volume of Representations and Birationality of Peripheral Holonomy ⋮ Local Rigidity for -Representations of 3-Manifold Groups ⋮ Complex hyperbolic geometry of the figure-eight knot ⋮ Fock-Goncharov coordinates for rank two Lie groups ⋮ Geometric structures and configurations of flags in orbits of real forms ⋮ Deformation Spaces of Discrete Groups of SU(2,1) in Quaternionic Hyperbolic Plane: A Case Study ⋮ Configurations of flags in orbits of real forms ⋮ Spherical CR uniformization of Dehn surgeries of the Whitehead link complement ⋮ The Ptolemy field of 3-manifold representations ⋮ Gluing equations for \(\mathrm{PGL}(n, \mathbb{C})\)-representations of 3-manifolds ⋮ Fundamental classes of 3-manifold groups representations in SL(4,R)

Uses Software

• ISOLATE

Cites Work

• Unnamed Item
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• Real hyperbolic on the outside, complex hyperbolic on the inside
• On the theories of triangular sets
• Complex hyperbolic geometry of the figure-eight knot
• Gluing equations for \(\mathrm{PGL}(n, \mathbb{C})\)-representations of 3-manifolds
• Rational univariate representations of bivariate systems and applications
• A VOLUME FUNCTION FOR SPHERICAL CR TETRAHEDRA
• SHARPER COMPLEXITY BOUNDS FOR ZERO-DIMENSIONAL GRÖBNER BASES AND POLYNOMIAL SYSTEM SOLVING
• Deformation of hyperbolic manifolds in 𝑃𝐺𝐿(𝑛,𝐂) and discreteness of the peripheral representations
• Local Rigidity for -Representations of 3-Manifold Groups
• Complex Kleinian groups
• Degenerating the complex hyperbolic ideal triangle groups

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