A geometric approach to Conn's linearization theorem

TL;DR

This paper presents a geometric proof of Conn's theorem, showing that certain Poisson structures can be simplified to linear form near singular points with compact semisimple isotropy Lie algebras.

Contribution

It provides a new geometric proof of a classical linearization result for Poisson structures around singular points.

Findings

Poisson structures are linearizable near specific singular points

The proof uses geometric methods rather than algebraic ones

The result applies to points with compact semisimple isotropy Lie algebras

Abstract

We give a soft geometric proof of the classical result due to Conn stating that a Poisson structure is linearizable around a singular point (zero) at which the isotropy Lie algebra is compact and semisimple.