Open book structures on semi-algebraic manifolds
| Autor: | Antonio Andrade do Espirito Santo, Ying Chen, R. Araújo Dos Santos, Nicolas Dutertre |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Marseille (I2M), Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU), Laboratoire Angevin de Recherche en Mathématiques (LAREMA), Université d'Angers (UA)-Centre National de la Recherche Scientifique (CNRS), Instituto de Ciências Mathemàticas e de Computação [São Carlos] (ICMC-USP), Universidade de São Paulo (USP), Instituto de Ciencias Matematicas e de Computaçao, Universidade de São Paulo (USP)-Universidade de São Paulo (USP), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Universidade de São Paulo = University of São Paulo (USP), Universidade de São Paulo = University of São Paulo (USP)-Universidade de São Paulo = University of São Paulo (USP) |
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
semi-algebraic manifolds
General Mathematics Dimension (graph theory) real Milnor fibrations Algebraic geometry 01 natural sciences symbols.namesake Mathematics - Algebraic Geometry Euler characteristic [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] FOS: Mathematics 0101 mathematics Algebraic Geometry (math.AG) Mathematics Mathematics - General Topology Discrete mathematics Homotopy 14P10 32S55 58K15 58K65 010102 general mathematics General Topology (math.GN) Fibration Manifold 010101 applied mathematics TOPOLOGIA ALGÉBRICA Projection (relational algebra) Number theory symbols [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] open book structure |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP manuscripta mathematica manuscripta mathematica, Springer Verlag, 2016, 149 (1), pp.18. ⟨10.1007/s00229-015-0772-4⟩ Manuscripta mathematica Manuscripta mathematica, 2016, 149 (1), pp.18. ⟨10.1007/s00229-015-0772-4⟩ |
| ISSN: | 0025-2611 1432-1785 |
| Popis: | International audience; Given a $C^2$ semi-algebraic mapping $F: \mathbb{R}^N \rightarrow \mathbb{R}^p,$ we consider its restriction to $W\hookrightarrow \mathbb{R^{N}}$ an embedded closed semi-algebraic manifold of dimension $n-1\geq p\geq 2$ and introduce sufficient conditions for the existence of a fibration structure (generalized open book structure) induced by the projection $\frac{F}{\Vert F \Vert}:W\setminus F^{-1}(0)\to S^{p-1}$. Moreover, we show that the well known local and global Milnor fibrations, in the real and complex settings, follow as a byproduct by considering $W$ as spheres of small and big radii, respectively. Furthermore, we consider the composition mapping of $F$ with the canonical projection $\pi: \mathbb{R}^{p} \to \mathbb{R}^{p-1}$ and prove that the fibers of $\frac{F}{\Vert F \Vert}$ and $\frac{\pi\circ F}{\Vert \pi\circ F \Vert}$ are homotopy equivalent. We also show several formulae relating the Euler characteristics of the fiber of the projection $\frac{F}{\Vert F \Vert}$ and $W\cap F^{-1}(0).$ Similar formulae are proved for mappings obtained after composition of $F$ with canonical projections. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink