Generalizations of local bijectivity of Keller maps and a proof of $2$-dimensional Jacobian conjecture

TL;DR

This paper proves the two-dimensional Jacobian conjecture by leveraging the local bijectivity property of Keller maps, providing a significant advancement in understanding polynomial map invertibility.

Contribution

It offers a novel proof of the 2D Jacobian conjecture based on local bijectivity of Keller maps, a new approach in the field.

Findings

Proof of the 2D Jacobian conjecture established

Local bijectivity of Keller maps confirmed as a key tool

Advances understanding of polynomial invertibility in two dimensions

Abstract

Using the local bijectivity of Keller maps, we give a proof of two-dimensional Jacobian conjecture.