Timeline for Why the Dold-Thom theorem?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Mar 7, 2016 at 20:14 | comment | added | მამუკა ჯიბლაძე | @lenticcatachresis Just a minor issue with basepoints, nothing serious. | |
| Mar 7, 2016 at 15:37 | comment | added | Bruno Stonek | @მამუკაჯიბლაძე: why is SP(X) only a free commutative topological monoid "of sorts"? Why the "of sorts"? | |
| Oct 23, 2014 at 19:07 | vote | accept | Chris Gerig | ||
| Oct 15, 2014 at 2:37 | comment | added | Dev Sinha | For intuition, I think a key is the first case of X a sphere. If one uses the model of a cube relative to its boundary, then the free abelian group on X is essentially the iterated bar construction, and so a model for an Eilenberg-MacClane space. | |
| Oct 8, 2014 at 7:20 | answer | added | Qiaochu Yuan | timeline score: 15 | |
| Oct 8, 2014 at 5:32 | answer | added | მამუკა ჯიბლაძე | timeline score: 18 | |
| Oct 7, 2014 at 22:38 | history | edited | Chris Gerig | CC BY-SA 3.0 |
added 585 characters in body
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| Oct 7, 2014 at 22:12 | answer | added | Ryan Budney | timeline score: 9 | |
| Oct 7, 2014 at 19:47 | comment | added | მამუკა ჯიბლაძე | @BenWieland yes, I agree. On the other hand I only mentioned the simplicial context as a sort of analogy, although it is also true that one might switch to it via, say, singular simplices and then relate Sing(SP(X)) to Z[Sing(X)]... | |
| Oct 7, 2014 at 19:27 | comment | added | Ben Wieland | @მამუკა ჯიბლაძე, I agree that is the right perspective, but you need a little bit more. $\mathbb Z[X]$ is a simplicial abelian group. There are two things you can do with it: turn it into a chain complex and take homology; or turn it into a space and take homotopy groups. You need to know that they correspond. This is sometimes included in Dold-Kan. | |
| Oct 7, 2014 at 19:09 | answer | added | Jesse C. McKeown | timeline score: 9 | |
| Oct 7, 2014 at 17:53 | comment | added | მამუკა ჯიბლაძე | Sort of intuitive heuristics behind the fact (for me) is that (a) SP(X) is the free commutative topological monoid on X (of sorts); (b) connected topological monoids possess homotopy inverses, so it is actually free topological abelian group on X (again sort of); (c) homology of X is more or less the same as homotopy of the free topological abelian group on X. All this is almost rigorous in the simplicial context, where $\tilde H_*(X)=\pi_*\mathbb Z[X]$, more or less by definition. | |
| Oct 7, 2014 at 17:48 | history | asked | Chris Gerig | CC BY-SA 3.0 |