Real polynomial maps and singular open books at infinity

Abstract

We provide significant conditions under which we prove the existence of stable open book structures at infinity, i.e. on spheres $S_R^{m-1}$ of large enough radius $R$. We obtain new classes of real polynomial maps ${\mathbb{R}}^m\to {\mathbb{R}}^p$ which induce such structures.

arXiv comment10p

References in corpus (5)

• Real map germs and higher open books
• Regularity at infinity of real mappings and a Morse-Sard theorem
• Invertible polynomial mappings via Newton non-degeneracy
• Bifurcation values and monodromy of mixed polynomials
• Milnor fibration and fibred links at infinity

Cited by in corpus (8)

• Fibrations of highly singular map germs
• Images of analytic map germs, and singular fibrations
• New examples of Neuwirth-Stallings pairs and non-trivial real Milnor fibrations
• Atypical points at infinity and algorithmic detection of the bifurcation locus of real polynomials
• Open book structures on semi-algebraic manifolds
• Global index of real polynomials
• Some remarks about $\rho$-regularity for real analytic maps
• Tame deformations of highly singular function germs