Complex projective space

Definition

Short definition

Complex projective space is defined as projective space over a field of complex numbers $\mathbb {C}$, where the topological structure is induced from the structure of the field of complex numbers as a topological field.

Algebraic topology

Homology

Further information: homology of complex projective space

Cohomology

Further information: cohomology of complex projective space

Homotopy

Further information: homotopy of complex projective space