Timeline for An abstract nonsense proof of the Hurewicz theorem
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 12, 2017 at 20:03 | answer | added | Gregory Arone | timeline score: 7 | |
| Oct 12, 2017 at 9:26 | comment | added | მამუკა ჯიბლაძე | @OscarRandal-Williams Why hide it - it turns out I actually don't know. I thought I knew but it turned out I never did. | |
| Oct 11, 2017 at 19:43 | answer | added | Anton Fetisov | timeline score: 10 | |
| Oct 11, 2017 at 18:25 | answer | added | Qiaochu Yuan | timeline score: 7 | |
| Oct 11, 2017 at 17:56 | comment | added | Oscar Randal-Williams | @მამუკაჯიბლაძე: How does this help you prove the Hurewicz theorem? | |
| Oct 11, 2017 at 4:55 | comment | added | მამუკა ჯიბლაძე | @DavidRoberts You are right, sorry, I meant "Simplicial objects in algebraic topology", Theorem 26.9 (on page 121) | |
| Oct 11, 2017 at 2:47 | answer | added | Jeff Strom | timeline score: 17 | |
| Oct 10, 2017 at 23:51 | comment | added | Ged Corob Cook | @anton I'd be interested to see the simple abstract proof, so that I can work out whether that's what I'm asking. | |
| Oct 10, 2017 at 23:27 | comment | added | Anton Fetisov | Hurewicz theorem is really the theorem about the homotopy category of spaces, thus the abstract $(\infty, 1)$-category of spaces is the proper setting for stating and proving it, and indeed it has a simple abstract proof. Is this what you're asking or are you really interested in the properties of the specific simplicial model? In the latter case you're bound to explicit computations. | |
| Oct 10, 2017 at 22:55 | comment | added | David Roberts♦ | @მამუკაჯიბლაძე that's a more than slightly ambiguous reference, tbh. | |
| Oct 10, 2017 at 20:59 | comment | added | მამუკა ჯიბლაძე | Pick a simplicial group model $G$ for the loop space of $X$, then the Hurewicz homomorphism is realized as that induced on $G\to G/[G,G]$. This is in many places, e. g. May | |
| Oct 10, 2017 at 20:54 | history | asked | Ged Corob Cook | CC BY-SA 3.0 |