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
DOI:
https://doi.org/10.1090/S0002-9939-08-09245-9
Published electronically:
April 23, 2008
MathSciNet review:
2407061
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: In this paper we consider the Jacobian conjecture for a map 
of complex affine spaces of dimension 
. It is well known that if 
is proper, then the conjecture will hold. Using topological arguments, specifically Smith theory, we show that the conjecture holds if and only if 
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:
https://doi.org/10.1090/S0002-9939-08-09245-9
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.