A note on the Jacobian conjecture
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- by Christopher I. Byrnes and Anders Lindquist PDF
- Proc. Amer. Math. Soc. 136 (2008), 3007-3011 Request permission
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.References
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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
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2407061