On Grothendieck's tame topology
| Autor: | A'Campo, Norbert, Ji, Lizhen, Papadopoulos, Athanase |
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| Přispěvatelé: | Mathematisches Institut, Universität Basel, Mathematisches Institut, Institut Mittag-Leffler, 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), Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA), ANR-12-BS01-0009,Finsler,Géométrie de Finsler et applications(2012) |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
semialgebraic geometry
moderate topology o-minimal structure Mathematics::Algebraic Geometry stratified structure semianalytic geometry subanalytic geometry [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] Modular multiplicity [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] 32G13 32G15 14H15 14C05 18A22 tame topology |
| Zdroj: | Handbook of Teichmüller theory, Volume VI Handbook of Teichmüller theory, Volume VI, 2016, Handbook of Teichmüller theory, Vol. VI, European Mathematical Society, Zurich, 2016, pp. 521--532., 978-3-03719-161-3. ⟨10.4171/161⟩ |
| DOI: | 10.4171/161⟩ |
| Popis: | International audience; Alexander Grothendieck, motivated by surface topology and moduli spaces of Riemann surfaces, calls in his in his ``Esquisse d'un programme" 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 Teichmüller 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. |
| Databáze: | OpenAIRE |
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