The fundamental group and Betti numbers of toric origami manifolds

TL;DR

This paper investigates the topology of orientable toric origami manifolds, determining their fundamental groups and Betti numbers, thereby advancing understanding of their geometric and topological properties.

Contribution

It provides the first determination of the fundamental group and Betti numbers for non-simply connected toric origami manifolds, extending previous cohomology results.

Findings

Fundamental group of orientable toric origami manifolds is characterized.

Betti numbers are computed for non-simply connected cases.

Extension of topological understanding beyond simply connected 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 oigami manifolds with coorientable folding hypersurface. We determine the fundamental group. In our previous paper [HP], we studied the ordinary and equivariant cohomology rings of simply connected toric origami manifolds. We conclude this paper by computing some Betti numbers in the non-simply connected case.