Timeline for Are there necessary and sufficient conditions for a chain complex $0 \to C_0 \to C_1 \to C_2 \to 0$ to be Poincare?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jan 20, 2016 at 22:28 | comment | added | Fernando Muro | Well, the tautological iff looks sufficient to me, and it is induced by a chain map since, over a PID, any chain complex is quasi-isomorphic to its homology. | |
| Jan 20, 2016 at 19:55 | comment | added | Najib Idrissi | Well it feels rather weird to say that something like $0 \to \mathbb{Z} \xrightarrow{=} \mathbb{Z} \to 0 \to 0$ satisfies Poincaré duality... | |
| Jan 20, 2016 at 18:13 | comment | added | Freddy | Yes, but I don't want to specify a map. | |
| Jan 20, 2016 at 17:46 | comment | added | Qiaochu Yuan | That seems like a weak condition. Wouldn't you rather these isomorphisms be induced by a map from the chain complex to the dual chain complex? | |
| Jan 20, 2016 at 17:37 | review | First posts | |||
| Jan 20, 2016 at 17:45 | |||||
| Jan 20, 2016 at 17:35 | history | asked | Freddy | CC BY-SA 3.0 |