Timeline for Constructing a simplicial set homology-equivalent to a given CW complex
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
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| Jul 7, 2012 at 11:23 | answer | added | BS. | timeline score: 1 | |
| Jul 6, 2012 at 23:42 | vote | accept | Vidit Nanda | ||
| Jul 6, 2012 at 23:25 | answer | added | Russ Woodroofe | timeline score: 2 | |
| Jul 3, 2012 at 3:26 | answer | added | Dan Ramras | timeline score: 2 | |
| Jul 3, 2012 at 3:06 | comment | added | Josh | That doesn't really answer my question, but I misread your OP. I saw "low dimensional homology" and you wrote "low dimensional CW complex". At any rate, you can get H_1 by abelianizing the group. For H_2, you might try the singular package on GAP, gap-system.org/Packages/simpcomp.html, or Javaplex, code.google.com/p/javaplex . | |
| Jul 3, 2012 at 1:23 | comment | added | Vidit Nanda | Josh: presentation groups are 2 dimensional, see (en.wikipedia.org/wiki/Presentation_complex) and you can build your own examples from finitely presented groups. Qiaochu: I don't need an explicit chain map, just isomorphic homology. | |
| Jul 3, 2012 at 0:19 | comment | added | Qiaochu Yuan | Do you only want the homology to be the same as a sequence of abelian groups or do you want there to exist a map that realizes an isomorphism on homology? | |
| Jul 3, 2012 at 0:08 | comment | added | Josh | How high of a dimension do you need to go? Can you give one example of a presentation of one of the groups you want to use? | |
| Jul 2, 2012 at 23:20 | history | edited | Vidit Nanda | CC BY-SA 3.0 |
Incorporated suggestions from the comments
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| Jul 2, 2012 at 20:32 | comment | added | Tyler Lawson | @Vel: The homotopy type of a cw complex is not determined by the degrees of the attaching maps of its cells (e.g. $\mathbb{CP}^2$). | |
| Jul 2, 2012 at 19:24 | comment | added | Fernando Muro | Vel, I've found the title misleading. Finding a homotopy equivalent (or just homology equivalent) simplicial set is not triangulating. | |
| Jul 2, 2012 at 18:23 | comment | added | Vidit Nanda | Igor: in this case, efficiency is not very important because the input has small size, both in terms of cell count and also in terms of the degrees of attaching maps. | |
| Jul 2, 2012 at 17:25 | comment | added | Igor Rivin | @Vel: I am asking because in many apsecial cases there are efficient algorithms for triangulation,which do not go through in general... | |
| Jul 2, 2012 at 17:20 | comment | added | Vidit Nanda | Igor, I am looking at presentation complexes of some small groups and of course the words in many relations contain exponents that are not $\pm 1$. I can add more detail if necessary, but I was trying to keep the question concise. | |
| Jul 2, 2012 at 17:12 | comment | added | Igor Rivin | Where do your cw complexes come from? | |
| Jul 2, 2012 at 16:56 | history | asked | Vidit Nanda | CC BY-SA 3.0 |