# On the Cohomology Ring of Real Moment-Angle Complexes

## TL;DR

This paper investigates the cohomology ring structure of real moment-angle complexes derived from simplicial complexes, providing explicit descriptions for boundary of polygons and highlighting differences from complex cases.

## Contribution

It offers a detailed combinatorial description of the cohomology ring for real moment-angle complexes, especially for polygon boundaries, revealing new structural insights.

## Key findings

- Cohomology generators are combinatorially described.
- Full multiplicative structure is characterized for polygon boundaries.
- Generators do not form a symplectic basis, unlike complex cases.

## Abstract

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.