[Merged by Bors] - feat: local inverse of a diffeomorphism#23219
Closed
[Merged by Bors] - feat: local inverse of a diffeomorphism#23219
Conversation
Add IsLocalDiffeomorphAt.localInverse, a (choice of) local inverse for a local diffeomorphism at x. Prove basic API about it: if f is a local diffeomorphism at x, we prove that - f and its local inverse near x are local inverses (in both directions), - composing f and its local inverse is EventuallyEq to the identity near x. - smoothness results for the local inverse. PR #8738 will use this to prove that the differential of a local diffeomorphism is a continuous linear equivalence.
PR summary d0e79dbd13Import changes for modified filesNo significant changes to the import graph Import changes for all files
|
This was referenced Mar 22, 2025
mathlib-bors bot
pushed a commit
that referenced
this pull request
Mar 25, 2025
Add IsLocalDiffeomorphAt.localInverse, a (choice of) local inverse for a local diffeomorphism at x. Prove basic API about it: if f is a local diffeomorphism at x, we prove that - f and its local inverse near x are local inverses (in both directions), - composing f and its local inverse is EventuallyEq to the identity near x. - smoothness results for the local inverse. PR #8738 will use this to prove that the differential of a local diffeomorphism is a continuous linear equivalence.
Contributor
|
Pull request successfully merged into master. Build succeeded: |
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
2 participants
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Add IsLocalDiffeomorphAt.localInverse, a (choice of) local inverse for a local diffeomorphism at x. Prove basic API about it: if f is a local diffeomorphism at x, we prove that
PR #8738 will use this to prove that the differential of a local diffeomorphism is a continuous linear equivalence.
I wondered if adding the analogous
IsLocalDiffeomorph.localInverseAtwould be useful: if so, I'll be happy to add it.