Simplifying singularities of Lagrangian projections

Dani Alvarez-Gavela proved an h-principle which allows to reduce singularities of Lagrangian caustics only to cusps provided that some necessary homotopical conditions are met. It turns out that even without any homotopical conditions singularities can be reduced, via a $C^0$-small Hamiltonian isotopy, to a finite list.

This is a part of our joint arborealization project with Dani Alvarez-Gavela and David Nadler.