Combinatorial methods in Teichmüller theory

Méthodes combinatoires en théorie de Teichmüller

Valentina Disarlo (1, 2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 SNS - Scuola Normale Superiore di Pisa

In this thesis we deal with combinatorial and geometric properties of arc complexes and triangulation graphs, and we will provide some applications to the study of the mapping class group and to the Teichmüller theory of a bordered surface. The thesis is divided into two parts. In the former we deal with the problem of combinatorial rigidity of arc complexes. In the latter we study some large-scale properties of the arc complex and the 1-skeleton of its dual, the so-called ideal triangulation graph.

Dans cette thèse nous étudions certains propriétés combinatoires et géométriques des complexes d'arcs des surfaces de type fini. Nous démontrons que le groupe d'automorphisme du complexe d'arcs est le mapping class group de la surface. Nous étudions aussi le graphe des triangulations idéales et nous donnons certains applications au espaces de Teichmueller des surfaces avec bord .

Keywords: mapping class group; Teichmueller space

Keywords: Espaces de Teichmüller

Domains: Geometric Topology [math.GT]

Valentina Disarlo. Combinatorial methods in Teichmüller theory. Geometric Topology [math.GT]. Scuola Normale Superiore; Université de Strasbourg, 2013. English. ⟨NNT : 2013STRAD017⟩. ⟨tel-00875029⟩