Anosov flows, surface groups and curves in projective space

By F. Labourie. 2004

532 citations recorded by the source corpus.

Note that in [10], W. Goldman gives a complete description of these connected components in the case of finite covers of PSL(2,R). In the case of PSL(2,R), two homeomorphic components, called Teichmuller spaces, play a central role. These two components are well known to be homeomorphic to a ball of dimension 6g − 6. N. Hitchin generalises this situation to PSL(n,R). Indeed, one of these components when n is odd, and two when n is even, has a very simple topology. Let us define an n-Fuchsian representation to be a representation ρ which can be written as ρ = ι ◦ ρ0, where ρ0 is a cocompact representation with values in PSL(2,R) and ι is the irreducible representation of PSL(2,R) in PSL(n,R), We denote by RepH(π1(S), PSL(n,R)) a connected component that contains Fuchsian representations, and call it a Hitchin component. In fact, when n is odd there is one Hitchin component, and when n is even two isomorphic ones. N. Hitchin proves in [17]

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/85db6d5816fc5df96adfcd9671441cd46fd43888

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Citations in the corpus

The pressure metric for Anosov representations (2013, background): “D G ] 2 1”
Compactification d’espaces de représentations de groupes de type fini (2010, background): “Si Γ = π1( ) et G = PSLn(R), alors d’après [24] et [28] la composante de Hitchin de l’espace des modules de G-fibrés plats sur est une composante connexe de X (Γ,G), incluse dans Xfd(Γ,G), et c’est une cellule de dimension (2g − 2) dim G.”
Zariski dense surface subgroups in SL(3,Z) (2011, background): “The results of Labourie [5] now imply that all of these deformations are discrete and faithful on K , and therefore discrete and faithful on ∆(3, 3, 4).”
Conformality for a robust class of non-conformal attractors (2019, background): “ to x,one has that for all i,xP αiC8pαiq,see Figure 2. 3. Anosov representations Anosov representations from fundamental groups of negatively curved closed manifoldstoPGLpd,Rq wereintroducedbyLabourie[37]andgeneralizedbyGuichardW.[28]toanyhyperbolicgroup. In this sectionwewillgeneralizetonon-Archime”
Higher Teichmüller Spaces: from SL(2,R) to other Lie groups (2010, background): “The proof for PSL(3,R) is independently due to Labourie [70] and Loftin [74].”
Anosov subgroups: dynamical and geometric characterizations (2017, background): “The class of Anosov subgroups, introduced by Labourie [25] and further extended by Guichard andWienhard [12], constitutes a natural generalization of convex cocompact subgroups of rank one Lie groups to higher rank.”
Convex cocompactness in pseudo-Riemannian hyperbolic spaces (2017, unknown): “[14]); they sharemany dynamical properties with classical convex cocompact subgroups of rank-one simple Lie groups (see in particular [30,34,35,38]).”