Timeline for Alternative approaches to the universal coefficient theorem
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 31, 2011 at 16:43 | comment | added | Greg Friedman | @Fernando - I'm not sure what that tells me about my question, though. Could you expand on that? - Thanks | |
| Aug 30, 2011 at 23:08 | comment | added | Fernando Muro | The derived category of a PID is the semidirect product of the category of graded modules and the shifted $Ext^1$ | |
| Aug 30, 2011 at 22:51 | comment | added | Greg Friedman | Hmmmm. But even an "unnatural splitting" must somehow arise out of the data at hand, right? And the only data present is a (homotopy class of a) chain map from A to I. So the only information present in computing, say, $H^0$ is a homomorphism $A^0\to Q(R)$, a homomorphism $A^1\to Q(R)/R$ and the boundary maps into and out of $A^0$ and $A^1$. Somehow that data must assemble to these groups, naturally or not, so I'd expect there must be a way to write down "the answer" in terms of that data. | |
| Aug 30, 2011 at 22:21 | comment | added | Tyler Lawson | If there was a "correct" map $H^*(Hom(A,I)) \to Hom(T^{1-*}(A), Q(R)/R)$, then the splitting in the universal coefficient sequence would be natural, no? | |
| Aug 30, 2011 at 19:51 | history | asked | Greg Friedman | CC BY-SA 3.0 |