Timeline for Manifold embedded in $R^{n+1}$ with a submanifold that doesn't embed in $R^n$
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Nov 8, 2016 at 22:31 | comment | added | Ryan Budney | Yes, I'm using "Euler class" in the sense of Whitney, i.e. with twisted coefficients. My impression is this is standard usage among 4-manifold theorists. | |
| Nov 8, 2016 at 22:21 | comment | added | Igor Belegradek | The unit normal bundle of the Klein bottle in $\mathbb R^4$ is non-orientable. Are you talking about the twisted Euler class? | |
| Nov 8, 2016 at 21:11 | comment | added | Ryan Budney | This is Danny's Klein bottle example, with $S^3 / Q8$ removed from the discussion. $S^3 / Q8$ is the unit normal bundle of any embedding of $\mathbb RP^2$ into $\mathbb R^4$ so they're very similar examples, in spirit. | |
| Nov 8, 2016 at 21:03 | history | answered | Ryan Budney | CC BY-SA 3.0 |