Timeline for Locally flat submanifold
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Apr 5, 2014 at 12:02 | comment | added | Benoît Kloeckner | See mathoverflow.net/questions/58061/… | |
| Apr 5, 2014 at 9:44 | history | edited | Ben McKay | CC BY-SA 3.0 |
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| Oct 29, 2011 at 23:03 | comment | added | Mariano Suárez-Álvarez | Please do not ask questions here and on math.stackexchange.com at the same time. math.stackexchange.com/questions/76977/locally-flat-submanifold | |
| Oct 29, 2011 at 1:26 | comment | added | Tom Goodwillie | Some authors use "submanifold" to mean what some other authors mean by "locally flat submanifold". Unfortunate, maybe, but undoubtedly true. | |
| Oct 29, 2011 at 1:18 | comment | added | Jim Conant | Another example: Take a knot $K$ in $S^3$ and consider the cone on the knot in $B^4$. This is a submanifold of $B^4$ homeomorphic to a disk, but it is not flat at the cone point. | |
| Oct 29, 2011 at 0:20 | comment | added | Ryan Budney | Either you misread the statement, or the author of the statement was wrong. IMO your question would maybe be more appropriate on math.stackexchange.com, as it seems like your question has more to do with interpreting standard point-set topology definitions. | |
| Oct 28, 2011 at 22:10 | comment | added | Antonio | I think you're wrong I read that the Horned Sphere is not a submanifold of $R^{3}$ | |
| Oct 28, 2011 at 21:58 | comment | added | Ryan Budney | Then Alexander's Horned Sphere is a submanifold of $\mathbb R^3$. | |
| Oct 28, 2011 at 21:54 | comment | added | Antonio | For me N is a d-dimensional submanifold of an n-dimensional manifold M if for every point x in N there exists an open subset of M such that x belongs to M and $U\cap N$ is homeomorphic to an open set in $R^{d}$ | |
| Oct 28, 2011 at 21:46 | comment | added | Mariano Suárez-Álvarez | You should tell us your definition of topological submanifold, probably. | |
| Oct 28, 2011 at 21:46 | comment | added | Ryan Budney | What definition of "submanifold" are you using? You've given a definition of "locally flat submanifold" but you haven't given a definition of "submanifold". | |
| Oct 28, 2011 at 21:35 | comment | added | Antonio | Alexander's Horned Sphere is not a submanifold of R^{3} is a manifold on its own but not a submanifold. Perhaps I dont understand the notion of locally flat submanifold. | |
| Oct 28, 2011 at 21:32 | comment | added | Ryan Budney | Alexander's Horned Sphere is technically an example of a topological subspace of a manifold which is also a manifold. So if that's your definition of "submanifold" then it qualifies. | |
| Oct 28, 2011 at 21:30 | comment | added | Ryan Budney | Alexander's Horned Sphere is the standard example, see any textbook on knot theory. Rolfsen's book has a detailed example. | |
| Oct 28, 2011 at 21:27 | history | asked | Antonio | CC BY-SA 3.0 |