The intrinsic topology of linear maps

2020/08/20 by Quan Xu, Xu, Quan
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2008.09101

openalex publication_date 2020/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Based on many experts' former work in the Jacobian conjecture and an essential analysis of intrinsic topology of linear maps, I completely prove the Jacobian conjecture by demonstrating the injectivity of real Keller map of any n-dimensions.

Citations

• A counterexamle to the strong real Jacobian conjecture

Related

• Generalizations of local bijectivity of Keller maps and a proof of 2-dimensional Jacobian conjecture
• Algebroids and Jacobian conjecture
• Injectivity of Keller Mappings
• Some Remarks on the Jacobian Conjecture and Connections with Hilbert's Irreducibility Theorem
• Generic degrees of real polynomial Keller maps with non-dense image