We study the existence problem of a dimensional Poincaré complex whose homology is isomorphic to that of dimensional complex projective space when .
Juno MUKAI. Kohhei YAMAGUCHI. "Homotopy classification of twisted complex projective spaces of dimension 4." J. Math. Soc. Japan 57 (2) 461 - 489, April, 2005. https://doi.org/10.2969/jmsj/1158242066