Symplectic automorphisms of CP^2 and the Thompson group T

TL;DR

This paper constructs a connection between birational automorphisms of the complex projective plane preserving a Poisson structure and the Thompson group T, providing new presentations and representations.

Contribution

It introduces a morphism linking birational automorphisms of CP^2 to Thompson group T and offers a new presentation of T in terms of generators and relations.

Findings

Constructed a morphism from birational automorphisms to T

Provided a linear representation of the automorphism group

Presented a new set of generators and relations for T

Abstract

We explain how to construct a morphism from the group of birational automorphisms of CP^2 preserving the logarithmic Poisson bracket to the Thompson group T. Than we give a linear representation of the former group, provide some information about Thompson group T and give it's new presentation in terms of generators and relations, and speculate about the presentation of the group of birational symplectomorphisms.