Cross ratios and identities for higher Teichmüller-Thurston theory

Cross ratios and identities for higher Teichmüller-Thurston theory

We generalise the McShane-Mirzakhani identities from hyperbolic geometry to arbitrary cross ratios. We define and study Hitchin representations of open surface groups to PSL ( n , R ) . We associate cross ratios to these representations and then give explicit expressions for our generalised identiti...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Duke mathematical journal 2009-08, Vol.149 (2), p.279-345
Hauptverfasser: Labourie, François, McShane, Gregory
Format: Artikel
Sprache:eng
Schlagworte:
30Fxx
32G07
32G15
Deformations of special (e.g. CR) structures
Moduli of Riemann surfaces
Teichmüller theory [See also 14H15
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We generalise the McShane-Mirzakhani identities from hyperbolic geometry to arbitrary cross ratios. We define and study Hitchin representations of open surface groups to PSL ( n , R ) . We associate cross ratios to these representations and then give explicit expressions for our generalised identities in terms of (a suitable choice of) Fock-Goncharov coordinates
ISSN:0012-7094
1547-7398
DOI:10.1215/00127094-2009-040