Timeline for What should I call a "differential" which cubes, rather than squares, to zero?
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| Nov 23, 2023 at 16:55 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Apr 18, 2020 at 18:23 | comment | added | AlexArvanitakis | @MikeMiller: thanks, that's good to know. The obvious generalisation to $D^p=0$ seems to have the same homology groups so your formula for $_kH(X)$ is a nice check | |
| Apr 18, 2020 at 18:14 | comment | added | mme | $\text{ker}(Q) = \text{ker}(D) \oplus \text{ker}(D^2)$. $\text{Im}(Q) = \text{Im}(D^2) \oplus \text{Im}(D)$. So your homology groups are (the direct sum of) those of Kapranov, which are in the case of $D^p = 0$, given as $_k H(X) = \text{ker}(D^k)/\text{Im}(D^{p-k})$. | |
| Apr 18, 2020 at 17:40 | history | edited | AlexArvanitakis | CC BY-SA 4.0 |
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| Apr 18, 2020 at 17:18 | history | answered | AlexArvanitakis | CC BY-SA 4.0 |