Timeline for Cubical vs. simplicial singular homology
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 19, 2020 at 21:24 | comment | added | Ronnie Brown | The paper arxiv:2001.00534 looks at the historical background, going back to the 1932 ICM at Zurich when Alexandroff and Hopf argued that E. Cech's seminar on higher homotopy groups was not suitable for a higher dimensional version of the fundamental group, because of their abelian nature. We now know that that problem can be resolved by moving from groups to groupoids, But simplicial methods have not yielded strict higher homotopy groupoids, analogous to the fundamental groupoid. See the paper referred to in my answer. | |
| Mar 9, 2019 at 11:31 | comment | added | Ronnie Brown | For evaluation of methods, one needs to consider what each can and cannot (so far) do, i.e. to evaluate successes against failures, and the significance of these in terms of the current and historical aims of the subject. | |
| Mar 6, 2019 at 3:20 | history | edited | Piotr Hajlasz | CC BY-SA 4.0 |
added 2 characters in body
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| Mar 5, 2019 at 14:31 | comment | added | mme | In fact, the homology of a point is already wrong! The boundary map is identically zero, but there is nonetheless a singular cube in each degree. So the naive cubical homology of a point is $\Bbb Z$ in each non-negative degree. | |
| Mar 1, 2019 at 17:42 | history | answered | Piotr Hajlasz | CC BY-SA 4.0 |