Timeline for Stable normal bundle and immersions
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 22, 2022 at 23:41 | history | became hot network question | |||
| Jun 22, 2022 at 16:26 | vote | accept | Overflowian | ||
| Jun 22, 2022 at 16:12 | history | edited | Michael Albanese | CC BY-SA 4.0 |
added 9 characters in body; edited tags
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| Jun 22, 2022 at 16:09 | answer | added | Michael Albanese | timeline score: 7 | |
| Jun 22, 2022 at 16:00 | comment | added | Overflowian | @kiran Thank you for your comment, I borrowed this def. from Cohen's notes. In general given an immersion $f:M\to N$, a virtual normal bundle for $f$ is a bundle $\nu$ such that $TM\oplus \nu \simeq f^*N$. In the above setting we are dealing with immersions into Euclidean spaces so we can say that $\nu$ is virtual normal bundle of rank $k$ if $TM\oplus \nu\simeq \varepsilon^{n+k}$, this implies by Hirsch-Smale theory that $M$ has an immersion into $\mathbb R^{n+k}$ with normal bundle isomorphic to $\nu$. If $k$ is large, $\nu$ is isomorphic to the stable normal bundle, for small $k$ idk. | |
| Jun 22, 2022 at 15:51 | comment | added | kiran | What's a "virtual normal bundle"? (it seems from your description of g that it's synonymous with "stable normal bundle"?) | |
| Jun 22, 2022 at 15:33 | history | asked | Overflowian | CC BY-SA 4.0 |