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Sep 24, 2020 at 23:21 comment added Michael Albanese Fake projective planes are irreducible. More generally, aspherical manifolds of dimension at least three are always irreducible.
Sep 23, 2020 at 3:25 comment added Ian Agol Kai, the fake projective planes only have the rational cohomology of $CP^2$, they have torsion in $H_1$. See Theorem 9.1 arxiv.org/abs/math/0512115v2
Sep 23, 2020 at 2:02 comment added Anubhav Mukherjee Can you please tell me the description of such algebraic surfaces which are fake projective spaces? Or any references?
Sep 22, 2020 at 23:44 history answered Kai Nakamura CC BY-SA 4.0