3 papers
math.SG2023
Coadjoint orbits of area-preserving diffeomorphisms of non-orientable surfaces
Anton Izosimov, Boris Khesin, Ilia Kirillov
We give a classification of generic coadjoint orbits for the group of area-preserving diffeomorphisms of a closed non-orientable surface. This completes V. Arnold's program of stud…
math.SG2020
Classification of coadjoint orbits for symplectomorphism groups of surfaces
Ilia Kirillov
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…
math.SG2018
Morse-Darboux lemma for surfaces with boundary
I. Kirillov
We formulate and prove an analog of the classical Morse-Darboux lemma for the case of a surface with boundary.