leanprover-community / leanprover-community/mathlib4
Generalize manifold structure on a vector bundle to a fiber bundle
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Description
One may want to consider fiber bundles with fibers that are not normed spaces.
It looks like at least parts of the construction already works for any fiber.
Note that SmoothVectorBundle is stronger than the (not yet defined)
SmoothBundle + (existing) VectorBundle because it requires
smoothness of coordChangeL, not just uncurry coordChange.
Contributor guide
First steps
- Read the whole issue, then the project's contributing guide.
- Comment on the issue to say you are picking it up — it saves two people doing the same work.
- Fork the repository and make your change on a branch.
- Open a pull request that references the issue number.
Research direction
Start by locating the existing SmoothVectorBundle and VectorBundle definitions and the construction of coordChangeL. Compare the current smoothness requirements with the proposed SmoothBundle abstraction; done means the fiber-independent construction and the relationship with VectorBundle are defined consistently.
Written by the indexing model from the issue text.
Assessment
- Domain
- tooling
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Stale
- Clarity
- Needs clarification
- Newbie friendliness
- 25/100