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A note on the Jacobian conjecture |
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| Authors: | Christopher I. Byrnes Anders Lindquist |
| Affiliation: | Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, Missouri 63130 Anders Lindquist ; Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden |
| 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. |
| Keywords: | Jacobian conjecture Smith theory. |
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