Timeline for Is cohomology always related to topology?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 16, 2021 at 13:22 | comment | added | Will Sawin | @xuq01 You can do lots of stuff with explicit definitions of cochains and differentials, just not everything. | |
| Jun 10, 2021 at 10:15 | comment | added | Sebastian Goette | Let me add Dolbeault cohomology of complex manifolds to the list. It contains subtle information about the complex structure. Of course, it can be turned into the cohomology of a certain sheaf on a topological space, but then the extra structure is hidden in that sheaf. | |
| Jun 10, 2021 at 7:37 | vote | accept | Nuno | ||
| Jun 10, 2021 at 7:37 | vote | accept | Nuno | ||
| Jun 10, 2021 at 7:37 | |||||
| Jun 9, 2021 at 22:50 | comment | added | xuq01 | Kudos for "cohomology is basically derived functors". Yes, it's really nearly impossible to discuss cohomology without category theory. In fact, I'm not a topologist/geometer, but I wonder if cohomology w/o all the CT is any good at all? | |
| Jun 9, 2021 at 20:17 | comment | added | paul garrett | I do like Weibel's book. @HollisWilliams, I think Weibel put an errata page on his web site. Do you mean that there are "many more" beyond that? | |
| Jun 9, 2021 at 20:13 | comment | added | Hollis Williams | By the way, the book of Weibel has a lot of typos and errors, just to warn people. | |
| Jun 9, 2021 at 14:38 | comment | added | Nuno | OK, thank you! By the way, I came across the nice book by Weibel "An Introduction to Homological Algebra" in case this is useful to others. | |
| Jun 9, 2021 at 14:08 | comment | added | Johannes Hahn | I would go even further and say that talking about cohomology in depth requires category theory, period. That is what category theory was invented for. The moment when you look at more than one cohomology theory, you will ask yourself "why do 1 and 2 look similar?" and "how can I use that similarity in order to save on proving everything yet again the third time?". Both questions are answered by category theory. | |
| Jun 9, 2021 at 14:07 | comment | added | Johannes Hahn | Just "cohomology" in general? No. That encompasses so much that there is little to say without heavy use of category theory I think. Everything I know or have read about cohomology in general fundamentally requires category theory. | |
| Jun 9, 2021 at 13:48 | comment | added | Nuno | Thank you @JohannesHahn, this is very helpful! Could you suggest an accessible reference on cohomology? (Ideally without a heavy use of category theory if this is possible :)) | |
| Jun 9, 2021 at 11:07 | history | answered | Johannes Hahn | CC BY-SA 4.0 |