Timeline for Topological operations corresponding to abelianization of the fundamental group
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Nov 6, 2021 at 17:42 | comment | added | Tyler Lawson | The canonical example of this is taking the infinite symmetric product of X, or the free topological abelian group on X: the Dold-Thom theorem. en.m.wikipedia.org/wiki/Dold%E2%80%93Thom_theorem | |
| Nov 6, 2021 at 13:01 | history | edited | Abh | CC BY-SA 4.0 |
deleted 87 characters in body
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| Nov 6, 2021 at 10:30 | comment | added | Denis Nardin | To elaborate on Maxime's message, Quillen's plus construction is not the universal map making the fundamental group abelian, but it is the universal map making the fundamental group hypoabelian, and in fact this often produces already the abelianization | |
| Nov 6, 2021 at 7:34 | history | edited | YCor | CC BY-SA 4.0 |
formatting, changed title (it looked like asking about a topology on the group itself)
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| Nov 6, 2021 at 0:28 | comment | added | Noah Snyder | Here's a related question. | |
| Nov 5, 2021 at 23:58 | comment | added | Donu Arapura | You could form the Eilenberg-MacLane space $X^{ab}= K(H_1(X,\mathbb{Z}),1)$, but this probably isn't the only choice satisfying your requirements. | |
| Nov 5, 2021 at 23:57 | comment | added | Maxime Ramzi | It's not exactly abelianization, but you might be interested in Quillen's +-construction. You can of course always add cells to $X$ to kill commutators in $\pi_1$, but I don't know if you'd like something more explicit (note that the +-construction is not that much more explicit, although it has a nice homotopical universal property) | |
| S Nov 5, 2021 at 23:45 | review | First questions | |||
| Nov 6, 2021 at 0:31 | |||||
| S Nov 5, 2021 at 23:45 | history | asked | Abh | CC BY-SA 4.0 |