Some Stably Tame Polynomial Automorphisms

Abstract

We study the structure of length three polynomial automorphisms of $R[X,Y]$ when $R$ is a UFD. These results are used to prove that if ${\text{SL}}_m(R[X_1,X_2,...,X_n])={\text{E}}_m(R[X_1,X_2,...,X_n])$ for all $n,\ge 0$ and for all $m\ge 3$ then all length three polynomial automorphisms of $R[X,Y]$ are stably tame.