The Amalgamated Product Structure of the Tame Automorphism Group in Dimension Three

Abstract

It is shown the the tame subgroup ${\text{TA}}_3(\mathbb{C})$ of the group ${\text{GA}}_3(\mathbb{C})$ of polynomials automorphisms of ${\mathbb{C}}^3$ can be realized as the product of three subgroups, amalgamated along pairwise intersections, in a manner that generalizes the well-known amalgamated free product structure of ${\text{TA}}_2(\mathbb{C})$ (which coincides with ${\text{GA}}_2(\mathbb{C})$ by Jung's Theorem). The result follows from defining relations for ${\text{TA}}_3(\mathbb{C})$ given by U. U. Umirbaev.

Cited by in corpus (2)

• The tame automorphism group of an affine quadric threefold acting on a square complex
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