The modular action on \(\mathrm{PSL}_2(\mathbb{R})\)-characters in genus 2

DOI10.1215/00127094-3166522zbMath1353.37056arXiv1309.3553OpenAlexW3103088995MaRDI QIDQ254771

Maxime Wolff, Julien Marché

Publication date: 16 March 2016

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

Full work available at URL: https://arxiv.org/abs/1309.3553

zbMATH Keywords

ergodicitymapping class groupscharacter varieties

Mathematics Subject Classification ID

Moduli problems for topological structures (58D29) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Fundamental group, presentations, free differential calculus (57M05) Teichmüller theory for Riemann surfaces (30F60)

Related Items

The symplectic structure for renormalization of circle diffeomorphisms with breaks ⋮ Mapping class group dynamics and the holonomy of branched affine structures ⋮ Geometrisation of purely hyperbolic representations in \(\mathrm{PSL}_2\mathbb{R}\) ⋮ Modular orbits on the representation spaces of compact abelian Lie groups ⋮ Almost strict domination and anti‐de Sitter 3‐manifolds ⋮ Ergodicity of the mapping class group action on Deroin-Tholozan representations ⋮ Quaternionic hyperbolic Fenchel-Nielsen coordinates ⋮ Simple length rigidity for Hitchin representations ⋮ Dynamics on the PSL(2,\(\mathbb{C}\))-character variety of a compression body ⋮ Six-point configurations in the hyperbolic plane and ergodicity of the mapping class group ⋮ On type-preserving representations of thrice punctured projective plane group

Cites Work

• Unnamed Item
• Unnamed Item
• The dynamics of \(\Aut(F_n)\) on redundant representations
• The Bers's constant in genus two
• The symplectic nature of fundamental groups of surfaces
• Topological components of spaces of representations
• Elementary geometry in hyperbolic space
• Branched \(\mathbb{C} P^ 1\)-structures on surfaces with prescribed real holonomy
• The modular group action on real \(SL(2)\)-characters of a one-holed torus
• The monodromy groups of Schwarzian equations on closed Riemann surfaces
• Groups acting on the circle.
• Geometry of the complex of curves. I: Hyperbolicity
• Compact anti-de Sitter 3-manifolds and folded hyperbolic structures on surfaces
• Remarks on the cohomology of groups
• Ergodicity of Mapping Class Group Actions on SU(2)-character varieties
• The Geometry of the Hyperelliptic Involution in Genus Two
• Markoff triples and quasifuchsian groups