On the Cohomology Ring of Real Moment-Angle Complexes

In this article, we study the cohomology ring of real moment-angle complexes over a simplicial complex K. Combinatorial generators for the cohomology can be given in terms of K. For K the boundary of an n-gon, we give a full description of the multiplicative structure of the cohomology ring in terms of the combinatorial generators. As a consequence, it is evident that these generators do not form a symplectic basis, unlike the case for moment-angle complexes.