On the Reduction Theorem for the Jacobian Conjecture

Abstract

The Jacobian Conjecture states that if a complex polynomial mapping has a Jacobian matrix whose determinant is a nonzero constant, it has an inverse, which is also a polynomial mapping. In this thesis, we consider the Reduction theorem by Bass, Connel, and Wright proposed in 1982, which states that we can reduce this conjecture to mappings of the form F=X+N, where N is cubic homogeneous. We compare this theorem to a paper written by Hubbers in 1999, who modified their technique to further reduce to a Druzkowski mapping.