The Poisson Linearization Problem for $\mathfrak{sl}_2(\mathbb{C})$

Ioan Marcut, Universitat zu Koln, Germany. Florian Zeiser, Institute for Basic Science-Center for Geometry and Physics, Pohang, South Korea

1. Poisson cohomology-Introduction; 1. The Poisson cohomology of $\mathfrak {sl}_2(\mathbb {C})$; 2. Flat foliated cohomology of $\mathfrak {sl}_2(\mathbb {C})$; 3. Homotopy operators for the foliated complex; 4. Flat Poisson cohomology of $\mathfrak {sl}_2(\mathbb {C})$; 2. The Nash-Moser method-Introduction; 5. A quantitative linearization theorem; 6. The sketch of the Nash-Moser algorithm; 7. Prerequisites; 8. The algorithm; 9. Proof of Theorem; A. Some decompositions of smooth functions on $\mathbb {C}$; B. Frechet spaces of smooth functions; C. Smoothing operators for flat functions