Goldman algebra, opers and the swapping algebra

DOI10.2140/gt.2018.22.1267zbMath1394.53086arXiv1212.5015OpenAlexW4291315643MaRDI QIDQ1746302

François Labourie

Publication date: 25 April 2018

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.5015

zbMATH Keywords

gauge theoryPoisson algebraTeichmüller theoryHitchin componentAtiyah-Bott-Goldman symplectic structureDrinfel'd-Sokolov reductionswapping algebra

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Poisson manifolds; Poisson groupoids and algebroids (53D17) Compact complex surfaces (32J15)

Related Items (3)

Rank \(n\) swapping algebra for Grassmannian ⋮ AdS 3-manifolds and Higgs bundles ⋮ Rank \(N\) swapping algebra for \({\operatorname{PGL}}_n\) Fock-Goncharov \(\mathcal{X}\) moduli space

Cites Work

• Lectures on representations of surface groups
• The pressure metric for Anosov representations
• Euler-Poincaré flows on \(\mathrm{sl}_{ n }\) opers and integrability
• Le spectre marqué des longueurs des surfaces à courbure négative. (The spectrum marked by lengths of surfaces with negative curvature)
• Cross ratios, surface groups, \(\text{PSL}(n,\mathbb R)\) and diffeomorphisms of the circle
• An algebra of observables for cross ratios
• Hitchin components and hyperconvex representations of surface groups
• On the symplectic geometry of deformations of a hyperbolic surface
• The symplectic nature of fundamental groups of surfaces
• Invariant functions on Lie groups and Hamiltonian flows of surface group representations
• The Fenchel-Nielsen deformation
• Separability properties of free groups and surface groups
• Lie groups and Teichmüller space
• On the cross-ratio at the boundary of \(CAT(-1)\)-spaces
• Lectures on classical \(W\)-algebras
• Higher-dimensional uniformisation and \(W\)-geometry
• Anosov representations: domains of discontinuity and applications.
• Sur la géométrie symplectique de l'espace des géodésiques d'une variété à courbure négative. (On the symplectic geometry of the space of geodesics of a manifold with negative curvature)
• Moduli spaces of local systems and higher Teichmüller theory
• Anosov flows, surface groups and curves in projective space
• Quantitative properties of convex representations
• The geometry of the KdV equation
• A simple model of the integrable Hamiltonian equation
• The Yang-Mills equations over Riemann surfaces
• Hyperconvex representations and exponential growth
• Cross ratios, Anosov representations and the energy functional on Teichmüller space

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