[Merged by Bors] - refactor(geometry/manifold): use a sigma type for the total space of the tangent bundle #3966
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sgouezel
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Co-authored-by: Nicolò Cavalleri <nico@cavalleri.net>
…ty/mathlib into sigma_tangent
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Somehow this is causing a timeout in |
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Fixed. |
hrmacbeth
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| end | ||
| /-- The canonical identification between the tangent bundle to the model space and the product, | ||
| as a homeomorphim -/ | ||
| def tangent_bundle_model_space_homeomorph : tangent_bundle I H ≃ₜ model_prod H E := |
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Presumably this could be a structomorphism? Would there be any benefit to registering that fact?
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@hrmacbeth thanks for taking a look! As I understand it, this is blocking the update of the LFTCM tutorials, so there's slight urgency here. (Let's not let those bitrot again.) If @PatrickMassot wants us to wait for a review, or if @sgouezel wants to wait for Patrick, that's fine. Otherwise let's get this in. bors d+ |
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✌️ sgouezel can now approve this pull request. To approve and merge a pull request, simply reply with |
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Let's get this in, then. It can still be refactored/improved later if needed. bors r+ |
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…the tangent bundle (#3966) Redefine the total space of the tangent bundle to be a sigma type instead of a product type. Before ``` have p : tangent_bundle I M := sorry, rcases p with ⟨x, v⟩, -- x: M -- v: E ``` After ``` have p : tangent_bundle I M := sorry, rcases p with ⟨x, v⟩, -- x: M -- v: tangent_space I x ``` This seems more natural, and is probably needed to do Riemannian manifolds right. The drawback is that we can not abuse identifications any more between the tangent bundle to a vector space and a product space (but we can still identify the tangent space with the vector space itself, which is the most important thing). Co-authored-by: Rob Lewis <Rob.y.lewis@gmail.com>
Co-authored-by: hrmacbeth <25316162+hrmacbeth@users.noreply.github.com>
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Canceled. |
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@sgouezel I'm at least going to commit Heather's typo fix first! bors r+ |
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…the tangent bundle (#3966) Redefine the total space of the tangent bundle to be a sigma type instead of a product type. Before ``` have p : tangent_bundle I M := sorry, rcases p with ⟨x, v⟩, -- x: M -- v: E ``` After ``` have p : tangent_bundle I M := sorry, rcases p with ⟨x, v⟩, -- x: M -- v: tangent_space I x ``` This seems more natural, and is probably needed to do Riemannian manifolds right. The drawback is that we can not abuse identifications any more between the tangent bundle to a vector space and a product space (but we can still identify the tangent space with the vector space itself, which is the most important thing). Co-authored-by: Rob Lewis <Rob.y.lewis@gmail.com>
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Oops, sorry! (and thanks, of course) |
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Pull request successfully merged into master. Build succeeded: |
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…the tangent bundle (#3966) Redefine the total space of the tangent bundle to be a sigma type instead of a product type. Before ``` have p : tangent_bundle I M := sorry, rcases p with ⟨x, v⟩, -- x: M -- v: E ``` After ``` have p : tangent_bundle I M := sorry, rcases p with ⟨x, v⟩, -- x: M -- v: tangent_space I x ``` This seems more natural, and is probably needed to do Riemannian manifolds right. The drawback is that we can not abuse identifications any more between the tangent bundle to a vector space and a product space (but we can still identify the tangent space with the vector space itself, which is the most important thing). Co-authored-by: Rob Lewis <Rob.y.lewis@gmail.com>
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…the tangent bundle (#3966) Redefine the total space of the tangent bundle to be a sigma type instead of a product type. Before ``` have p : tangent_bundle I M := sorry, rcases p with ⟨x, v⟩, -- x: M -- v: E ``` After ``` have p : tangent_bundle I M := sorry, rcases p with ⟨x, v⟩, -- x: M -- v: tangent_space I x ``` This seems more natural, and is probably needed to do Riemannian manifolds right. The drawback is that we can not abuse identifications any more between the tangent bundle to a vector space and a product space (but we can still identify the tangent space with the vector space itself, which is the most important thing). Co-authored-by: Rob Lewis <Rob.y.lewis@gmail.com>
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Redefine the total space of the tangent bundle to be a sigma type instead of a product type. Before
After
This seems more natural, and is probably needed to do Riemannian manifolds right. The drawback is that we can not abuse identifications any more between the tangent bundle to a vector space and a product space (but we can still identify the tangent space with the vector space itself, which is the most important thing).