Abstract:
A nonlinear flag in a manifold $M$ is a nested set of closed submanifolds $$N_1\subseteq\dots\subseteq N_r\subseteq M.$$
We study the geometry of the (Fr'echet) manifolds of nonlinear flags,generalizations of nonlinear Grassmannians.
We show how they appear as coadjoint orbits of the Hamiltonian group (joint work with Stefan Haller).
Low dimensional nonlinear flag manifolds endowed with suitable metrics can be used as shape spaces (joint work with Barbara Tumpach).