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Jacobian Conjecture and semi-algebraic maps

Published online by Cambridge University Press:  23 June 2014

ALEXANDRE FERNANDES ,
CARLOS MAQUERA  and
JEAN VENATO–SANTOS
ALEXANDRE FERNANDES
Affiliation:
Departamento de Matemática, Universidade Federal do Ceará, 13560-970, Fortaleza-CE, Brazil. e-mail: alexandre.fernandes@ufc.br
CARLOS MAQUERA
Affiliation:
Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo - Campus de São Carlos, 13560-970, São Carlos-SP, Brazil. e-mail: cmaquera@icmc.usp.br
JEAN VENATO–SANTOS
Affiliation:
Faculdade de Matemática, Universidade Federal de Uberlândia, 38408-100, Uberlândia-MG, Brazil. e-mail: jvenatos@famat.ufu.br
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Abstract

Let F:${\mathbb R}$n→${\mathbb R}$n be a polynomial local diffeomorphism and let SF denote the set of not proper points of F. The Jelonek's real Jacobian Conjecture states that if codim(SF) ≥ 2, then F is bijective. In this work we prove a weak version of such Conjecture, but for more general maps than polynomial, namely: the semi-algebraic maps.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 157 , Issue 2 , September 2014 , pp. 221 - 229
Copyright
Copyright © Cambridge Philosophical Society 2014 

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