Timeline for Why the choice of the simplex for defining homology?
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
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| Apr 25, 2023 at 16:47 | comment | added | The Amplitwist | Reposting a link mentioned in the previous comment so that it appears in the "Linked" questions list: Simplicial objects | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| May 23, 2010 at 17:40 | vote | accept | Akela | ||
| May 18, 2010 at 3:31 | comment | added | Reid Barton | This question is closely related: mathoverflow.net/questions/691/simplicial-objects | |
| May 17, 2010 at 12:56 | history | edited | Akela | CC BY-SA 2.5 |
added 1045 characters in body
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| May 17, 2010 at 12:12 | answer | added | Urs Schreiber | timeline score: 1 | |
| May 17, 2010 at 3:31 | comment | added | Daniel Moskovich | I think that the answer is en.wikipedia.org/wiki/Simplicial_set I wish I understood it better than I do, because it looks to me like the reason simplices are "nice" is extremely fundamental and transcends topology or context-specific requirements. At a completely category-theoretic level, degeneracies and face maps are fundamental (Hopf algebra structure in some strange way?) | |
| May 16, 2010 at 23:45 | comment | added | Mariano Suárez-Álvarez | Well... Boundary maps in cubes come from excluding a single coordinate :) | |
| May 16, 2010 at 22:43 | answer | added | Greg Kuperberg | timeline score: 22 | |
| May 16, 2010 at 22:22 | comment | added | S. Carnahan♦ | I don't think we need a fancy explanation - simplices are just easy to use. Boundary maps on chains come from excluding a single vertex. | |
| May 16, 2010 at 22:18 | comment | added | Dan Piponi | Lots of constructions are elegant with simplices. Like the fact that the simplices of a barycentric subdivion correspond to the possible orderings of the vertices of the parent simplex. | |
| May 16, 2010 at 22:09 | comment | added | Steve Huntsman | I'm no expert, but my understanding is that the simplicial approach to singular homology is essentially historical and associated with triangulations. While one can "triangulate" w/r/t cubes or disks, the combinatorial aspects of triangulation via simplicies are considerably simpler for abstract or generic situations. And as I understand it, the early work in combinatorial/algebraic topology was done with simplices. | |
| May 16, 2010 at 21:31 | history | asked | Akela | CC BY-SA 2.5 |