Timeline for Are homotopy equivalent submanifolds also cobordant?
Current License: CC BY-SA 3.0
8 events
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| Aug 6, 2017 at 20:10 | comment | added | Mark Grant | A similar question was asked here: mathoverflow.net/questions/27702/… Note that the homotopy $f$ already gives a null-bordism of $A\cup B$, so you just have to decide if $f$ can be made an immersion (for which there is the Smale-Hirsch theory) and then an embedding (for which there are variants of the Whitney trick, as mentioned in Oscar's answer, but these will be highly sensitive to the dimension/codimension). | |
| Aug 6, 2017 at 18:08 | history | edited | DanielHarlow | CC BY-SA 3.0 |
changed continuous to $C^1$ since implicitly the question used immersions.
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| Aug 6, 2017 at 18:01 | history | edited | DanielHarlow | CC BY-SA 3.0 |
modified to include a point form the comments.
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| Aug 6, 2017 at 17:45 | comment | added | DanielHarlow | You mean because the derivative matrix of $f$ might not have full rank? Or did you have some other obstruction in mind? | |
| Aug 6, 2017 at 17:42 | history | edited | DanielHarlow | CC BY-SA 3.0 |
added 7 characters in body
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| Aug 6, 2017 at 17:42 | comment | added | John Pardon | The version of the question for immersions does not have an obvious answer as you suggest it does. You can't always make a map an immersion using general position arguments. | |
| Aug 6, 2017 at 17:33 | history | edited | DanielHarlow | CC BY-SA 3.0 |
switched "homologous" to "cobordant", which is more accurate.
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| Aug 6, 2017 at 17:26 | history | asked | DanielHarlow | CC BY-SA 3.0 |