Timeline for reference for (co)homology theories
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 12, 2014 at 0:00 | vote | accept | seub | ||
| Nov 25, 2012 at 20:17 | comment | added | Mariano Suárez-Álvarez | Your point 2 is covered in pretty much any exposition which mentions two of the cohomology theories... If a text mentions two of these cohomologies is generally to connect them, because that is the whole point of having two constructions for the same thing! | |
| Nov 25, 2012 at 20:02 | answer | added | Deane Yang | timeline score: 1 | |
| Nov 25, 2012 at 17:25 | history | edited | user9072 |
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| Nov 24, 2012 at 20:23 | answer | added | R.P. | timeline score: 2 | |
| Nov 23, 2012 at 18:03 | comment | added | Callan McGill | The notes of Bruzzo above discuss what he calls the abstract de-Rham theorem and how this is related to the usual De-Rham theorem à la Donu Arapura's answer. The corresponding theorem for Dolbeault cohomology is also indicated. | |
| Nov 23, 2012 at 15:57 | answer | added | Donu Arapura | timeline score: 7 | |
| Nov 23, 2012 at 9:26 | answer | added | daniele | timeline score: 3 | |
| Nov 23, 2012 at 8:57 | comment | added | seub | Hi guys, thank you for your suggestions! After a brief peak though, it seems to me that these references are pretty much of two types: either more or less classical treatments of algebraic topology (e.g. Bruzzo, Hatcher); or homological algebra, categories and group cohomology (e.g. Weibel, Gelfand-Manin). I am not sure either are what I'm looking for. Agreed, Bott and Tu's seems interesting too, but it doesn't cover several of "my" cohomology theories. In particular, none of these books seem to care too much about request 2. Maybe I'm asking too much? | |
| Nov 23, 2012 at 8:20 | answer | added | Thomas Rot | timeline score: 3 | |
| Nov 23, 2012 at 7:42 | comment | added | Dan Petersen | You might be looking for Gelfand and Manin's "Homological Algebra". Here's a downloadable version: math.unam.mx/javier/AlgebraV.pdf | |
| Nov 23, 2012 at 4:49 | answer | added | paul garrett | timeline score: 3 | |
| Nov 23, 2012 at 3:57 | comment | added | skupers | What about Bott & Tu's Differential Forms in Algebraic Topology? It covers singular and de Rham in detail, and sheaf cohomology somewhat, and spends quite a bit of time relating these and giving examples of computations. | |
| Nov 23, 2012 at 1:10 | comment | added | algori | seub -- all the theories you mention (singular, de Rham, Dolbeault, group cohomology, sheaf cohomology) are particular cases of sheaf cohomology, for which there are many references; if you're after a quick and informal introduction that skips some proofs but still conveys the main ideas I would suggest e.g. Kirwan and Woolf's Oxford lecture notes on intersection homology. Now, you also mention cohomology theories, which is a slightly different thing. It is very carefully explained e.g. in Switzer's Algebraic topology but I find the presentation a bit tedious. | |
| Nov 23, 2012 at 0:43 | comment | added | Callan McGill | This could be worthwhile to you: people.sissa.it/~bruzzo/notes/IATG/notes.pdf | |
| Nov 23, 2012 at 0:33 | history | asked | seub | CC BY-SA 3.0 |