Timeline for Intuition behind Thom class
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 23, 2012 at 15:47 | comment | added | Tom Goodwillie | I've deleted it now. Of course I like your advanced viewpoint; I just couldn't see it as an answer to the question. Your answer could be fleshed out to make the point that the (reduced) ordinary cohomology of $S^n$ vanishes in degrees less than $n$ (i.e. that the coefficient groups of ordinary cohomology vanish in positive degrees), which is what makes the existence of a Thom class follow from the existence of an orientation. The same point could be made in a less advanced way using a spectral sequence rather than parametrized spectra. | |
| Sep 23, 2012 at 15:45 | comment | added | Tom Goodwillie | Yes, it's hard that comments can't be edited. I carelessly lost one set of words in dividing the comment, and I also carelessly forgot to mention the local triviality hypothesis. | |
| Sep 22, 2012 at 17:11 | comment | added | Peter May | Tom, your comment is incomplete and needs editing. The theorem that is unstated needs its hypotheses (compatibity on intersections) as well as its statement. But of course the point that local implies global fails for generalized cohomology is part of what I had in mind. (While the question implicitly refers to ordinary cohomology, that is not explicit, so it seemed not unreasonable to give a general answer). | |
| Sep 22, 2012 at 13:18 | history | answered | Peter May | CC BY-SA 3.0 |