Thurston's metric on Teichmüller space and isomorphisms between Fuchsian groups

Athanase Papadopoulos (1) , Weixu Su (2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 Fudan University [Shanghai]

The aim of this paper is to relate Thurston's metric on Teichmüller space to several ideas initiated by T. Sorvali on isomorphisms between Fuchsian groups. In particular, this will give a new formula for Thurston's asymmetric metric for surfaces with punctures. We also update some results of Sorvali on boundary isomorphisms of Fuchsian groups.

Mots clés: Thurston's metric; Teichmüller space; Fuchsian group; boundary mapping; translation length.; translation length

Domaines: Topologie géométrique [math.GT]

Athanase Papadopoulos, Weixu Su. Thurston's metric on Teichmüller space and isomorphisms between Fuchsian groups. 2012. ⟨hal-00740320⟩