Classification of coadjoint orbits for symplectomorphism groups of surfaces

TL;DR

This paper classifies generic coadjoint orbits and simple Morse functions for symplectomorphism groups of compact surfaces, advancing understanding of symplectic surface symmetries.

Contribution

It provides a comprehensive classification of coadjoint orbits and Morse functions for symplectomorphism groups on surfaces, a novel result in symplectic geometry.

Findings

Classification of generic coadjoint orbits for symplectomorphism groups

Classification of simple Morse functions up to symplectomorphism

Extension to surfaces with and without boundary

Abstract

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.