(see also Chern-Weil theory, parameterized homotopy theory)
vector bundle, (∞,1)-vector bundle
topological vector bundle, differentiable vector bundle, algebraic vector bundle
direct sum of vector bundles, tensor product of vector bundles, inner product of vector bundles?, dual vector bundle
The concept of projective bundle is the generalization of that of projective space from vector spaces to vector bundles.
For $\pi \colon E \to X$ a topological vector bundle over some topological field $k$, write $E \setminus X \subset E$ for its complement of the zero section, regarded with its subspace topology.
Then its projective bundle is the fiber bundle $P(E) \to X$ whose total space the quotient topological space of $E \setminus X$ by the equivalence relation
hence
and whose bundle projection is
Last revised on May 29, 2017 at 03:32:56. See the history of this page for a list of all contributions to it.