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On topological approaches to the Jacobian conjecture in ℂn
Part of:
Affine geometry
Partial differential equations
Theory of singularities and catastrophe theory
Differential topology
General first-order equations and systems
Families, fibrations
Published online by Cambridge University Press: 07 May 2020
Abstract
We obtain a new theorem for the non-properness set 
$S_f$ of a non-singular polynomial mapping 
$f:\mathbb C^n \to \mathbb C^n$. In particular, our result shows that if f is a counterexample to the Jacobian conjecture, then 
$S_f\cap Z \neq \emptyset $, for every hypersurface Z dominated by 
$\mathbb C^{n-1}$ on which some non-singular polynomial 
$h: \mathbb C^{n}\to \mathbb C$ is constant. Also, we present topological approaches to the Jacobian conjecture in 
$\mathbb C^n$. As applications, we extend bidimensional results of Rabier, Lê and Weber to higher dimensions.
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 63 , Issue 3 , August 2020 , pp. 666 - 675
- Copyright
- Copyright © The Authors, 2020. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society
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