Timeline for Is a retract of a group of type F_n again of this type?
Current License: CC BY-SA 3.0
9 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Aug 12, 2013 at 11:52 | vote | accept | Werner Thumann | ||
| Aug 12, 2013 at 11:52 | answer | added | Werner Thumann | timeline score: 2 | |
| May 21, 2013 at 8:36 | comment | added | Werner Thumann | Thank you, Misha. I will have a closer look at the material and argument you proposed. | |
| May 17, 2013 at 19:48 | comment | added | Misha | A brief proof is that a group is of type $F_n$ if and only if it is coarsely $n-1$-connected. (I am almost sure Ross has this in his book, if not, we have it in our lectures on geometric group theory.) A Lipschitz retraction applied to the coarse $k$-th homotopy group implies vanishing for the subgroup, by the same argument as for the usual homotopy groups. | |
| May 17, 2013 at 19:10 | comment | added | Werner Thumann | Tanks for your comment, Misha. I checked the book before I posted the question, but I couldn't find it. Maybe I'm just blind. | |
| May 17, 2013 at 19:02 | comment | added | Misha | Yes, this is true. Check Geoghegan's book "Topological methods in group theory". If it is not there, I can write a proof at MO. Once you set up the correct (pro) homotopy groups for this problem, the proof becomes essentially the same as for the statement that a retract of an $n$-connected space is also $n$-connected. | |
| May 17, 2013 at 18:42 | history | edited | Werner Thumann | CC BY-SA 3.0 |
deleted 4 characters in body
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| May 17, 2013 at 18:18 | history | asked | Werner Thumann | CC BY-SA 3.0 |