Cohomological Rigidity of the Connected Sum of Three Real Projective Spaces

A real toric manifold $X^{\Bbb R}$ is said to be cohomologically rigid over ${\Bbb Z} _2$ if every real toric manifold whose ${\Bbb Z} _2$-cohomology ring is isomorphic to that of $X^{\Bbb R}$ is actually diffeomorphic to $X^{\Bbb R}$. Not all real toric manifolds are cohomologically rigid over ${\Bbb Z} _2$. In this paper, we prove that the connected sum of three real projective spaces is cohomologically rigid over ${\Bbb Z} _2$.