THE HOROFUNCTION COMPACTIFICATION OF THE ARC METRIC ON TEICHMÜLLER SPACE

Daniele Alessandrini (1) , Lixin Liu (2) , Athanase Papadopoulos (3) , Weixu Su (4)

1 Universität Heidelberg [Heidelberg] = Heidelberg University
2 SYSU - Sun Yat-sen University [Guangzhou]
3 IRMA - Institut de Recherche Mathématique Avancée
4 Fudan University

The arc metric is an asymmetric metric on the Teichmüller space T(S) of a surface S with nonempty boundary. In this paper we study the relation between Thurston's compactification and the horofunction compactification of T(S) endowed with the arc metric. We prove that there is a natural homeomorphism between the two compactifications.

Mots clés: Arc metric; horofunction; horoboundary; Thurston's asymmetric metric; measured lamination; measured foliation; Thurston's compactification; Teichmüller space; horofunction boundary

Domaines: Topologie géométrique [math.GT]

Daniele Alessandrini, Lixin Liu, Athanase Papadopoulos, Weixu Su. THE HOROFUNCTION COMPACTIFICATION OF THE ARC METRIC ON TEICHMÜLLER SPACE. 2016. ⟨hal-01086187v2⟩