Open book structures on semi-algebraic manifolds

Author(s)

Dutertre, N. ^[1] ; Araujo dos Santos, R. N. ^[2] ; Chen, Ying ^[2] ; do Espirito Santo, Antonio Andrade ^[3]

Affiliation

^[1] Aix Marseille Univ, CNRS, Cent Marseille, I2M, UMR 7373, F-13453 Marseille - France

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil

^[3] Univ Fed Reconcavo Bahia, Ctr Ciencias Exatas & Tecnol, BR-44380000 Cruz Das Almas, BA - Brazil

• Document type: Journal article
• Source: MANUSCRIPTA MATHEMATICA; v. 149, n. 1-2, p. 205-222, JAN 2016.
• Web of Science Citations: 1

Abstract

Given a C (2) semi-algebraic mapping , we consider its restriction to an embedded closed semi-algebraic manifold of dimension and introduce sufficient conditions for the existence of a fibration structure (generalized open book structure) induced by the projection . 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 and prove that the fibers of and are homotopy equivalent. We also show several formulae relating the Euler characteristics of the fiber of the projection and . Similar formulae are proved for mappings obtained after composition of F with canonical projections. (AU)

• FAPESP's process: 12/18957-7 - Study of singularities for mixed polynomials
• Grantee: Ying Chen
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 13/23443-5 - Topology of the fibers of real and complex polynomials mappings: local and global (at infinity) aspects
• Grantee: Raimundo Nonato Araújo dos Santos
• Support Opportunities: Regular Research Grants