THE TOPOLOGY OF TORIC ORIGAMI MANIFOLDS

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 symplectic manifolds, studied by Cannas da Silva, Guillemin and Pires, who classified toric origami manifolds by combinatorial origami templates. In this paper, we examine the topology of toric origami manifolds that have acyclic origami template and coorientable folding hypersurface. We prove that the cohomology is concentrated in even degrees, and that the equivariant cohomology satisfies the Goresky, Kottwitz and MacPherson description. Finally, we show that toric origami manifolds with coorientable folding hypersurface provide a class of examples of Masuda and Panov's torus manifolds.