A Proof of the Plane Jacobian Conjecture

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The paper is withdrawn.

This paper has been withdrawn by the author.

This paper has been withdrawn by the author due to a crucial argument error at p.10.

Major mistake. The paper has been withdrawn.

A non-zero constant Jacobian polynomial maps $F=(P,Q)$ of $\mathbb{C}^2$ is invertible if $P$ and $Q$ are rational polynomials.

This paper has been withdrawn by the author due a few mistakes in the paper.

This paper has been withdrawn by the author.

The paper was withdrawn by the author. It contained various errors.

This paper has been withdrawn by the author due to some errors.