Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Yucai Su

Abstract

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

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

Abstract

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

Paper Structure

This paper contains 12 sections, 31 theorems, 284 equations.

Table of Contents

  1. Main theorem
  2. Proofs of Theorems \ref{['Theo-2']} and \ref{['Theo-3']}
  3. Some preparations
  4. Proof of Theorem \ref{['Theo-2']}
  5. Proof of Theorem \ref{['Theo-3']} provided by Claudio Procesi
  6. Proof of Theorem \ref{['MAINT']}
  7. Two propositions
  8. Proof of Proposition \ref{['real00-inj+1']} provided by Claudio Procesi and proof of Theorem \ref{['MAINT']}
  9. Proof of Proposition \ref{['real00-inj']}
  10. Another proof of surjectivity of $\pi_1$
  11. Another proof of Proposition \ref{['real00-inj+1']}
  12. A proposition provided by Bin Xu

Key Result

Theorem 1.1

The Keller map $\sigma$ is injective. Consequently, the $2$-dimensional Jacobian conjecture holds.

Theorems & Definitions (55)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Remark 2.1
  • Remark 2.2
  • Definition 2.4
  • Lemma 2.5
  • Lemma 2.6
  • Remark 2.7
  • Lemma 2.8
  • ...and 45 more