Equivariant Chern Classes of Orientable Toric Origami Manifolds

A toric origami manifold, introduced by Cannas da Silva, Guillemin and Pires, is a generalization of a toric symplectic manifold. For a toric symplectic manifold, its equivariant Chern classes can be described in terms of the corresponding Delzant polytope and the stabilization of its tangent bundle splits as a direct sum of complex line bundles. But in general a toric origami manifold is not simply connected, so the algebraic topology of a toric origami manifold is more difficult than a toric symplectic manifold. In this paper they give an explicit formula of the equivariant Chern classes of an oriented toric origami manifold in terms of the corresponding origami template. Furthermore, they prove the stabilization of the tangent bundle of an oriented toric origami manifold also splits as a direct sum of complex line bundles.