Timeline for Homotopy of Brown-Gitler spectra
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 21 at 10:49 | answer | added | Neil Strickland | timeline score: 7 | |
| Sep 21 at 6:59 | comment | added | categorically_stupid | @JonathanBeardsley thanks for the comment, the comparison with Eilenberg-Maclane spectra is especially helpful. I was hoping that there might be a slick way to use the fact that they filter bo in homology and turn this into a statement about homotopy, but I guess that's a little too much to ask for. | |
| Sep 21 at 6:57 | comment | added | categorically_stupid | @NicholasKuhn that is a good point. Thank you for the comment. | |
| Sep 21 at 6:17 | comment | added | Jonathan Beardsley | So in this case you've controlled the homology and lost control of the homotopy groups. The other thing to keep in mind is that to build an EM spectrum you attach a ton of cells. | |
| Sep 21 at 6:13 | comment | added | Jonathan Beardsley | In my experience there's a tension between homology and homotopy. Homology "counts cells" so it's simpler for things with few cells. But this makes the homotopy groups blow up in complexity. On the other hand, if you control the homotopy groups, e.g. Eilenberg-MacLane spectra, then the homology becomes very hard to compute. | |
| Sep 21 at 3:26 | comment | added | Nicholas Kuhn | One can essentially never calculate many of the homotopy groups (stable or unstable) of a finite complex. (When k=2, one is looking at the homotopy groups of the real projective plane.) | |
| Sep 20 at 20:02 | history | asked | categorically_stupid | CC BY-SA 4.0 |