Timeline for When do chain complexes decompose as a direct sum?
Current License: CC BY-SA 2.5
16 events
| when toggle format | what | by | license | comment | |
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| May 27, 2015 at 6:16 | answer | added | Saurabh Singh | timeline score: 0 | |
| Jul 23, 2010 at 19:08 | history | edited | Dylan Wilson | CC BY-SA 2.5 |
edited title
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| Jul 23, 2010 at 7:03 | vote | accept | Dylan Wilson | ||
| Jul 22, 2010 at 7:32 | comment | added | Dylan Wilson | I've changed the statement of the problem to avoid confusion (I hope!) | |
| Jul 22, 2010 at 7:31 | history | edited | Dylan Wilson | CC BY-SA 2.5 |
changed question statement terminology to avoid confusion
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| Jul 22, 2010 at 7:12 | comment | added | Victor Protsak | I am not sure about the homotopy category of complexes, but in the module category and general additive category the right term to use would be "decompose", not split (cf "indecomposable module"). | |
| Jul 22, 2010 at 0:52 | answer | added | Tom Goodwillie | timeline score: 5 | |
| Jul 22, 2010 at 0:04 | answer | added | Greg Stevenson | timeline score: 5 | |
| Jul 21, 2010 at 23:49 | answer | added | Tony Scholl | timeline score: 3 | |
| Jul 21, 2010 at 23:43 | history | edited | Dylan Wilson | CC BY-SA 2.5 |
Took out confusing example taht didn't apply and clarified definition
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| Jul 21, 2010 at 23:42 | comment | added | Dylan Wilson | Oh, Greg I see your point! I was quoting Weibel, but that was before he was working in the homotopy category. I'll edit the question to take that out and clarify what I mean by "split". Thanks! | |
| Jul 21, 2010 at 23:34 | comment | added | Tom Goodwillie | No, don't worry, I just wanted to make sure. Reading between the lines, I think that by "does this chain complex split?", you mean "is it the direct sum of two (nonzero? acyclic?) chain complexes?" | |
| Jul 21, 2010 at 22:52 | comment | added | Greg Stevenson | So you are asking about how to detect when a complex $A$ decomposes nontrivially as $A_1 \oplus A_2$? The comment about acyclic complexes is a little confusing if this is what you mean since any bounded acyclic complex of projective $R$-modules is contractible. | |
| Jul 21, 2010 at 22:29 | comment | added | Dylan Wilson | Uh oh- is there a difference between the notions: split as in has a splitting map and split as in decomposes as a direct sum of chain complexes? Because I mean the latter, but I thought they were the same... | |
| Jul 21, 2010 at 22:25 | comment | added | Tom Goodwillie | Can you please say what you mean by split? I have some guesses, but I'm not at all confident that I know. | |
| Jul 21, 2010 at 21:59 | history | asked | Dylan Wilson | CC BY-SA 2.5 |