The fundamental group and Betti numbers of toric origami manifolds

Abstract

Toric origami manifolds are characterized by origami templates, which are combinatorial models built by gluing polytopes together along facets. In this paper, we examine the topology of orientable toric origami manifolds with coorientable folding hypersurface. We determine the fundamental group. In our previous paper, we studied the ordinary and equivariant cohomology rings of simply connected toric origami manifolds. We conclude this paper by computing some Betti numbers and cohomology rings in the non-simply connected case.