Produção Nacional
Revisado por pares
Open book structures on semi-algebraic manifolds
2015; Springer Science+Business Media; Volume: 149; Issue: 1-2 Linguagem: Inglês
10.1007/s00229-015-0772-4
ISSN1432-1785
AutoresNicolas Dutertre, Raimundo N. Araújo dos Santos, Ying Chen, Antonio Andrade do Espirito Santo,
Tópico(s)Algebraic structures and combinatorial models
ResumoGiven 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.
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