Toric origami manifolds and origami templates

A folded symplectic form on a manifold is a closed 2-form with the mildest possible degeneracy along a hypersurface. A special class of folded symplectic manifolds are the origami manifolds. In the classical case, toric symplectic manifolds can classified by their moment polytope, and their topology (equivariant cohomology) can be read directly from the polytope. In this talk we examine the toric origami case: we will describe how toric origami manifolds can also be classified by their combinatorial moment data, and present some results about the topology of toric origami manifolds. Feedback on the "right" combinatorial questions to ask will be very much appreciated. This is joint work with Ana Rita Pires.