Parameterizing Hitchin components

DOI10.1215/0012794-2838654zbMath1326.32023arXiv1209.3526OpenAlexW3098255364MaRDI QIDQ488068

Guillaume Dreyer, Francis Bonahon

Publication date: 23 January 2015

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.3526

zbMATH Keywords

positive representationgeodesic laminationAnosov representationHitchin componentHitchin representationshear invariant

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Teichmüller theory for Riemann surfaces (30F60)

Related Items (17)

Coordinates on the augmented moduli space of convex RP2 structures ⋮ Length functions of Hitchin representations ⋮ Weakly positive and directed Anosov representations ⋮ McShane Identities for Higher Teichmüller Theory and the Goncharov–Shen Potential ⋮ Higher spin JT gravity and a matrix model dual ⋮ Degeneration of Hitchin representations along internal sequences ⋮ Pressure metrics for cusped Hitchin components ⋮ Hitchin representations of Fuchsian groups ⋮ The area of convex projective surfaces and Fock–Goncharov coordinates ⋮ The Goldman and Fock-Goncharov coordinates for convex projective structures on surfaces ⋮ Deforming convex real projective structures ⋮ The real spectrum compactification of character varieties: characterizations and applications ⋮ Shearing deformations of Hitchin representations and the Atiyah-Bott-Goldman symplectic form ⋮ Degeneration of strictly convex real projective structures on surfaces ⋮ Flows on the PGL(V)-Hitchin component ⋮ Continuity of the SRB entropy of convex projective structures ⋮ Positive configurations of flags in a building and limits of positive representations

Cites Work

• Length functions of Hitchin representations
• The pressure metric for Anosov representations
• Cross ratios and identities for higher Teichmüller-Thurston theory
• Convex real projective structures on compact surfaces
• Topological components of spaces of representations
• Lie groups and Teichmüller space
• Shearing hyperbolic surfaces, bending pleated surfaces and Thurston's symplectic form
• Hitchin characters and geodesic laminations
• Anosov representations: domains of discontinuity and applications.
• Moduli spaces of local systems and higher Teichmüller theory
• Anosov flows, surface groups and curves in projective space
• Parabolic Higgs bundles and Teichmüller spaces for punctured surfaces
• Combinatorics of Train Tracks. (AM-125)
• Geometric Invariant Theory
• Convex Real Projective Structures on Closed Surfaces are Closed
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