Grothendieck's Reconstruction Principle and 2-dimensional Topology and Geometry

On Grothendieck's tame topology

Grothendieck's Esquisse d'un programme is often referred to for the ideas it contains on dessins d'enfants, the Teichm{ü}ller tower, and the actions of the absolute Galois group on these objects or their etale fundamental groups. But this program contains several other important ideas. In particular, motivated by surface topology and moduli spaces of Riemann surfaces, Grothendieck calls there for a recasting of topology, in order to make it fit to the objects of semialgebraic and semianalytic geometry, and in particular to the study of the Mumford-Deligne compactifications of moduli spaces. A …

Actions of the Absolute Galois Group

We review some ideas of Grothendieck and others on actions of the absolute Galois group Γ Q of Q (the automorphism group of the tower of finite extensions of Q), related to the geometry and topology of surfaces (mapping class groups, Teichm{ü}ller spaces and moduli spaces of Riemann surfaces). Grothendieck's motivation came in part from his desire to understand the absolute Galois group. But he was also interested in Thurston's work on surfaces, and he expressed this in his Esquisse d'un programme, his R{é}coltes et semailles and on other occasions. He introduced the notions of dessin d'enfant…

相对双曲群、格罗滕迪克对与纤维积中不可数的投射有限歧义

Relatively hyperbolic groups, Grothendieck pairs, and uncountable profinite ambiguity among fibre products

本文研究相对双曲群直积的投射有限刚性丧失问题，提出构造无限格罗滕迪克对和不可数互不同构子群族的一般方法，并以Weeks流形基本群和8字结补4重分支覆盖基本群为例，证明格罗滕迪克对完全解释了其直积的刚性丧失。