(see also Chern-Weil theory, parameterized homotopy theory)
homotopy theory, (∞,1)-category theory, homotopy type theory
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see also algebraic topology
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Given two vector bundles and , then their external tensor product is the tensor product of vector bundles on the product space of the two pullback bundles to this space, along the canonical projection maps .
More abstracty, this is the external tensor product in the indexed monoidal category of vector bundles indexed over suitable spaces.
Let and be topological spaces and let and be topological vector bundles.
The product topological space comes with two continuous projection functions
This gives rise to the pullback bundles and .
The external tensor product is the tensor product of vector bundles of these pullback bundles:
which is again naturally a vector bundle over th product space
(external product theorem in topological K-theory)
For a compact Hausdorff space then the external tensor product of vector bundles over and over the 2-sphere is an isomorphism of topological K-theory rings:
Last revised on September 27, 2021 at 11:59:13. See the history of this page for a list of all contributions to it.