Timeline for Recognizing regular neighborhoods
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 20, 2010 at 18:06 | answer | added | Greg Kuperberg | timeline score: 2 | |
| Jul 19, 2010 at 14:23 | history | edited | Igor Belegradek | CC BY-SA 2.5 |
added 1323 characters in body
|
| Jul 19, 2010 at 4:21 | comment | added | Igor Belegradek | The submanifolds are smooth, but the union of their $r$-neighborhoods is not a smooth submanifold, hence we are forced to leave smooth category. I am using the usual PL regular neighborhoods. You are correct that it is enough to realize the neighborhood as a mapping cylinder of some retraction; how do you do that? | |
| Jul 19, 2010 at 4:12 | comment | added | Ryan Budney | What definition of regular neighbourhood do you want to use? It sounds like you're in a mixed smooth and PL category? In the smooth category (where I think your question might have a simple answer) a regular neighbouhood of a subset $X$ can be taken to be a smooth neighbourhood $U$ that is a mapping cylinder from the boundary manifold $\partial U$ to the set $X$. If that's all you're after, then I think you can construct the regular neighbourhood from the tubular neighbourhood of your indivitual manifolds. | |
| Jul 19, 2010 at 3:33 | history | asked | Igor Belegradek | CC BY-SA 2.5 |