The torsion of real toric manifolds

Abstract

In view of various results and the nature of their constructions for real toric objects, it is an interesting and also natural problem to know how much torsion can be contained in their cohomology groups. The aim of this paper is to answer this question by explicitly constructing examples of real toric objects to show the richness of torsion which can appear in the cohomology groups with coefficients in a locally constant presheaf. That is, we show that a real quasitoric manifold (or small cover) which plays an important role in the category of real toric objects can have an arbitrary amount of torsion in its cohomology groups with coefficients in a locally constant presheaf. This will be achieved by crucially using the Torsion Theorem for links of Bosio and Meersseman.