On Grothendieck's tame topology
| Autor: | A'Campo, Norbert, Ji, Lizhen, Papadopoulos, Athanase |
|---|---|
| Přispěvatelé: | Mathematisches Institut, Universität Basel, Mathematisches Institut, Department of Mathematics - University of Michigan, University of Michigan [Ann Arbor], University of Michigan System-University of Michigan System, Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
o-minimal structure
stratified structure semianalytic geometry Geometric Topology (math.GT) Mathematics - Logic modular multiplicity semialgebraic geometry 32G13 32G15 14H15 14C05 18A22 Mathematics - Geometric Topology Mathematics - Algebraic Geometry moderate topology [MATH.MATH-LO]Mathematics [math]/Logic [math.LO] Mathematics::Algebraic Geometry subanalytic geometry [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] FOS: Mathematics [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] Logic (math.LO) Algebraic Geometry (math.AG) tame topology |
| Popis: | Grothendieck's Esquisse d'un programme is often referred to for the ideas it contains on dessins d'enfants, the Teichm{\"u}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 new conception of manifold, of submanifold and of maps between them is outlined. We review these ideas in the present chapter, because of their relation to the theory of moduli and Te-ichm{\"u}ller spaces. We also mention briefly the relations between Grothendieck's ideas and earlier theories developed by Whitney, Lojasiewicz and Hironaka and especially Thom, and with the more recent theory of o-minimal structures. The final version of this paper will appear as a chapter in Volume VI of the Handbook of Teichm{\"u}ller theory. This volume is dedicated to the memory of Alexander Grothendieck. |
| Databáze: | OpenAIRE |
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