A glimpse into Thurston's work

Ken'Ichi Ohshika (1) , Athanase Papadopoulos (2, 3)

1 Department of Mathematics [Gakushuin]
2 GREAM - Groupe de recherches expérimentales sur l'acte musical
3 IRMA - Institut de Recherche Mathématique Avancée

We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book ``In the tradition of Thurston: Geometry and topology", edited by K. Ohshika and A. Papadopoulos (Springer, 2020).

Mots clés: foliation; contact structure; symplectic structure; conformal geometry; holomorphic motion; Kleinian groups; circle packing; automatic groups; tiling; mapping class groups; Teichmüller space; fashion design; linkage; Anti-de Sitter geometry; higher Teichmüller theory; Grothendieck-Thurston theory; asymmetric metric; Schwarzian derivative; computer science; Ehrenpreis conjecture; transitional geometry; 3-manifolds; geometric structures; (G; X)-structures; Dehn surgery; hyperbolic geometry; Thurston norm; Smith conjecture; Cannon-Thurston map; discrete conformal geometry; discrete Riemann mapping theorem AMS codes

Domaines: Topologie géométrique [math.GT]; Histoire et perspectives sur les mathématiques [math.HO]

Ken'Ichi Ohshika, Athanase Papadopoulos. A glimpse into Thurston's work. 2020. ⟨hal-02936616v1⟩