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A note on the Jacobian conjecture
Author(s):
Christopher
I.
Byrnes;
Anders
Lindquist
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3007-3011.
MSC (2000):
Primary 14R15, 55M35;
Secondary 47H10
Posted:
April 23, 2008
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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:
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
Posted:
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
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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