Timeline for Boundary map for Mayer-Vietoris sequence for Bordism
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 23, 2020 at 12:26 | comment | added | Raghav | @GregFriedman, that part is guaranteed by the statement of the transversality theorem (such as on pg 24, appendix 2, Stong's "Notes on Cobordism theory"). It homotopes the continuous map $\phi\circ f$ to a smooth map $\tilde{\phi}$ that is moreover transverse regular on 0, so that the inverse image is indeed a submanifold of codimension 1. I have fixed this in the question, now | |
| Feb 23, 2020 at 12:23 | history | edited | Raghav | CC BY-SA 4.0 |
added 7 characters in body
|
| Feb 23, 2020 at 4:34 | comment | added | Greg Friedman | You have to be a bit more careful in your argument since your statements about transversality require smoothness or some other hypotheses (or fancier theorems). In general, this kind of issue can make it hard to show that certain bordism theories really are homology theories, at least by hands on arguments. | |
| Feb 22, 2020 at 14:15 | comment | added | Raghav | ok, coincidentally I have managed to find a reference after having randomly clicked on some link a few minutes after posting that made some reference to a book by Tom Dieck. And indeed there it is, on page 523, what I am looking for! (maths.ed.ac.uk/~v1ranick/papers/diecktop.pdf) | |
| Feb 22, 2020 at 13:49 | history | asked | Raghav | CC BY-SA 4.0 |