Timeline for Existence of a chain map lifting the identity; Alexander-Whitney/Eilenberg-Zilber maps
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 4, 2012 at 19:46 | vote | accept | James Miller | ||
| Jun 3, 2012 at 5:44 | comment | added | James Miller | If you consider only the mappings $\Pi \rightarrow \mathbb{Z}$ with finite support, then the two definitions of group ring ought to coincide. | |
| Jun 3, 2012 at 5:11 | answer | added | Andrew Ranicki | timeline score: 3 | |
| Jun 3, 2012 at 5:02 | comment | added | Tom Church | Incidentally, it seems you are confusing the group ring $\mathbb{Z}\Pi$ (the group of formal linear combinations of elements of $\Pi$) with its dual (the group of functions from $\Pi$ to $\mathbb{Z}$). For a finite group like $\Pi=\mathbb{Z}/2\mathbb{Z}$ there is not a huge difference, but for infinite groups the distinction is very important. For example, if $\Pi$ is countably infinite, the group ring $\mathbb{Z}\Pi$ will be countably infinite, while its dual is uncountable! | |
| Jun 3, 2012 at 3:37 | history | edited | James Miller | CC BY-SA 3.0 |
edited body
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| Jun 3, 2012 at 3:35 | comment | added | Sean Tilson | so you need to define a chain map by specifying its values on each $e_i$. Use the fact that is a chain map so you know... this should help. Also, this question is more appropriate for math.stackexchange.com | |
| Jun 3, 2012 at 2:37 | history | edited | James Miller | CC BY-SA 3.0 |
added 26 characters in body; edited title
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| Jun 3, 2012 at 2:20 | history | asked | James Miller | CC BY-SA 3.0 |