Timeline for What is (co)homology, and how does a beginner gain intuition about it?
Current License: CC BY-SA 2.5
20 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 2 at 13:03 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Mar 20, 2019 at 14:38 | comment | added | Student | @HarrisonBrown IMO that is because the natural structure of a set of functions (algebra) is easier to manipulate than the natural structure of a set of spaces (co-algebra). | |
| Mar 9, 2016 at 16:27 | comment | added | Margaret Friedland | related question:mathoverflow.net/questions/60108/… | |
| Oct 27, 2009 at 8:27 | history | edited | Greg Stevenson |
edited tags
|
|
| Oct 20, 2009 at 5:16 | vote | accept | Qiaochu Yuan | ||
| Oct 15, 2009 at 23:43 | comment | added | Aaron Mazel-Gee | Implicit in Reid's answer is the fact that cohomology has a product structure instead of just a group structure, which (for example) I believe can be used to distinguish spaces whose cohomologies are the isomorphic as <i>groups</i> but not as <i>rings</i>. | |
| Oct 15, 2009 at 21:57 | answer | added | Ilya Grigoriev | timeline score: 60 | |
| Oct 15, 2009 at 21:23 | vote | accept | Qiaochu Yuan | ||
| Oct 15, 2009 at 21:24 | |||||
| Oct 15, 2009 at 21:15 | answer | added | Mikael Vejdemo-Johansson | timeline score: 5 | |
| Oct 15, 2009 at 21:11 | answer | added | Mikael Vejdemo-Johansson | timeline score: 11 | |
| Oct 15, 2009 at 21:04 | answer | added | Mikael Vejdemo-Johansson | timeline score: 9 | |
| Oct 15, 2009 at 20:51 | comment | added | Reid Barton | Homology has to do with taking the free abelian group on a set, while cohomology has to do with taking the ring of functions on a set. Algebraic geometry is all about treating an arbitrary ring as the ring of functions on something, so it's not surprising that algebraic geometers care a lot about cohomology. | |
| Oct 15, 2009 at 20:46 | answer | added | Reid Barton | timeline score: 57 | |
| Oct 15, 2009 at 20:42 | answer | added | Eric Wofsey | timeline score: 20 | |
| Oct 15, 2009 at 20:37 | answer | added | David Lehavi | timeline score: 2 | |
| Oct 15, 2009 at 20:20 | comment | added | Harrison Brown | One sub-question you didn't mention but which interests me: Why, on a basic level, do mathematicians use cohomology more than homology, or at least talk about it more? I've developed a tentative opinion on this, but I'm always excited to hear what others have to say. | |
| Oct 15, 2009 at 20:13 | answer | added | Kevin H. Lin | timeline score: 27 | |
| Oct 15, 2009 at 20:03 | answer | added | Harrison Brown | timeline score: 9 | |
| Oct 15, 2009 at 19:55 | answer | added | Andy Putman | timeline score: 5 | |
| Oct 15, 2009 at 19:49 | history | asked | Qiaochu Yuan | CC BY-SA 2.5 |