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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on the Jacobian conjecture


Authors: Christopher I. Byrnes and Anders Lindquist
Journal: Proc. Amer. Math. Soc. 136 (2008), 3007-3011
MSC (2000): Primary 14R15, 55M35; Secondary 47H10
Published electronically: April 23, 2008
MathSciNet review: 2407061
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Abstract: In this paper we consider the Jacobian conjecture for a map $ f$ of complex affine spaces of dimension $ n$. It is well known that if $ f$ is proper, then the conjecture will hold. Using topological arguments, specifically Smith theory, we show that the conjecture holds if and only if $ f$ is proper onto its image.


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Additional Information

Christopher I. Byrnes
Affiliation: Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, Missouri 63130

Anders Lindquist
Affiliation: Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09245-9
PII: S 0002-9939(08)09245-9
Keywords: Jacobian conjecture, Smith theory.
Received by editor(s): October 25, 2006
Published electronically: April 23, 2008
Additional Notes: This research was supported in part by grants from AFOSR, NSF, the Swedish Research Council, and the Göran Gustafsson Foundation.
Communicated by: Paul Goerss
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.