Projective Spaces

Abstract

Coming from algebraic geometry, projective spaces and their Hopf bundles play an important role in homotopy theory, as already seen in Sects. 3.8 and 4.3 . The precise knowledge of their cohomology algebra has interesting applications, like the Borsuk-Ulam theorem, continuous multiplications in $${\mathbb R}^m$$ and the Hopf invariant, which are presented in Sect. 6.2.