Complex Projective Plane - Topology

Topology

The Betti numbers of the complex projective plane are

1, 0, 1, 0, 1, 0, 0, .....

The middle dimension 2 is accounted for by the homology class of the complex projective line, or Riemann sphere, lying in the plane. The nontrivial homotopy groups of the complex projective plane are . The fundamental group is trivial and all other higher homotopy groups are those of the 5-sphere, i.e. torsion.