Lesson plan
Pullback bundle
In mathematics, a pullback bundle or induced bundle is the fiber bundle that is induced by a map of its base-space. Given a fiber bundle \pi:E\rightarrow B and a continuous map f:B'\rightarrow B one can define a "pullback" of E by f as a bundle f^*E over B' . The fiber of f^*E over a point b' in B' is just the fiber of E over f(b') . Thus f^*E is the disjoint union of all these fibers equipped with a suitable topology.
Article summary
In mathematics, a pullback bundle or induced bundle is the fiber bundle that is induced by a map of its base-space. Given a fiber bundle \pi:E\rightarrow B and a continuous map f:B'\rightarrow B one can define a "pullback" of E by f as a bundle f^*E over B' . The fiber of f^*E over a point b' in B' is just the fiber of E over f(b') . Thus f^*E is the disjoint union of all these fibers equipped with a suitable topology.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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