Timeline for Elementary proof of the uniqueness of smooth structures on $\mathbb{R}$
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jun 28 at 5:55 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Jun 28 at 5:55 | comment | added | YCor | Uniqueness means "uniqueness modulo homeomorphism" i.e. any two smooth structures are conjugate by some homeomorphism, or equivalently that any two smooth structures define diffeomorphic smooth manifolds. | |
| Jun 27 at 16:45 | history | edited | LSpice | CC BY-SA 4.0 |
Remove "thank you", while this is on the front page
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| Jun 27 at 16:03 | answer | added | Sergiy Maksymenko | timeline score: 1 | |
| Jan 22, 2015 at 13:45 | comment | added | Ben McKay | Use bump functions to make a complete metric, a 2-1 cover to make a unit vector field, and then map a time variable to the manifold by flowing a point along the vector field: your manifold has the real line as universal covering space, and the covering map is an isometry. Work out the groups of isometries of the real line that act freely without fixed points. | |
| Jan 21, 2015 at 4:13 | vote | accept | Tatin | ||
| Jan 13, 2015 at 22:06 | comment | added | Ryan Budney | The classification of 1-manifolds up to diffeomorphisms has a proof that uses little more than existence and uniqueness to solutions of C^1 ODEs. That gives a perhaps more pleasant proof than thinking about charts. | |
| Jan 13, 2015 at 21:11 | history | edited | Ricardo Andrade |
replaced deprecated tag 'geometry'
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| Jan 13, 2015 at 13:56 | answer | added | Will Sawin | timeline score: 8 | |
| Jan 13, 2015 at 12:27 | comment | added | Alex Degtyarev | The very concept of smooth structure and diffeomorphism is way beyond undergraduate real analysis. | |
| Jan 13, 2015 at 12:25 | history | asked | Tatin | CC BY-SA 3.0 |