Classification of Coadjoint Orbits for Symplectomorphism Groups of Surfaces

We classify generic coadjoint orbits for symplectomorphism groups of compact symplectic surfaces with or without boundary. We also classify simple Morse functions on such surfaces up to a symplectomorphism.

Automated summary

This article focuses on the classification of generic coadjoint orbits for symplectomorphism groups of compact symplectic surfaces with or without boundary. It also classifies simple Morse functions on such surfaces up to a symplectomorphism.