A real toric space is a topological space which admits a well-behaved \Z_2^k-action.

Real moment-angle complexes, real toric varieties and small covers are typical examples of real toric spaces.

A real toric space is determined by the pair of a simplicial complex K and a characteristic matrix \Lambda.

In this talk, we discuss an explicit -cohomology ring formula of a real toric space in terms of K and \Lambda, where R is a commutative ring with unity in which 2 is a unit. Interestingly, it has a natural (\Z \oplus \row \Lambda)-grading.

This...