The topology of smooth projective planes

(i) If the (covering) dimension n of the point space ~ is finite, then ~ is a generalized manifold, and N has the same cohomology as one of the four classical point spaces P2 N, P2t~, P2]H or P2 O, and thus n e {2, 4, 8, 16}, cp. L6wen [111. This holds in particular, if the point rows and the pencils of lines are topological manifolds. In this case, the point rows and pencils of lines are n/2-spheres, cp. Salzmann [14, 7.12], Breitsprecher [2, 2.1]. It is not known whether the point rows have to be topological manifolds even if the point space is a topological manifold. (ii) If the (covering) dimension of the point space ~ is 2 or 4, then the point rows and the pencils of lines are topological manifolds, cp. Salzmann [14, 2.0] [15, 1.1], and .~ is homeomorphic to P2 N or PzlE, respectively, cp. Salzmann [14, 2.0], Breitsprecher [2, 2.5].