The complex Hopf fibration is the principal circle bundleIt is the unit-sphere bundle of the tautological complex line bundle.
Its mod-two cohomology ring iswhere is the mod-two reduction of the first Chern class of the dual tautological complex line bundle.
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Complex projective space, denoted as \(\mathbb{CP}^n\), is a fundamental concept in complex geometry and algebraic geometry. It is a space that generalizes the idea of projective space to complex numbers.