Timeline for Distinct, non-homeomorphic, profinite topologies on a given abstract group ?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 26, 2011 at 12:40 | vote | accept | Stephan F. Kroneck | ||
| Apr 24, 2011 at 13:47 | answer | added | Jonathan Kiehlmann | timeline score: 4 | |
| Apr 24, 2011 at 9:19 | answer | added | Yiftach Barnea | timeline score: 3 | |
| Apr 23, 2011 at 23:59 | comment | added | Ian Agol | For finitely generated profinite groups, the uniqueness of the topology follows from a result of Nikolov and Segal (see mathoverflow.net/questions/34290/…). | |
| Apr 23, 2011 at 22:35 | comment | added | Stephan F. Kroneck | @ Pete L. Clark: Dear Pete, it seems just adding my name in the ID-box took care that matter (no loss of history). Furthermore, I started reading your lecture notes on transcendental Galois Theory, and am wondering whether you would have any pertinent remarks concerning my other question posted (regarding an Artin-style approach to infinite Galois Theory), as you are obviously well-versed in that area ? Kind regards, Stephan. | |
| Apr 23, 2011 at 22:32 | comment | added | Pete L. Clark | @Stephan: it's no "harm" to use a pseudonym. It's probably just "better" (in my opinion and the opinion of many, but not all, members of the site) to use your real name unless you have a specific reason not to. For instance, if I or someone else meets you in real life, we can make the (positive!) connection to the person who asked/answered questions on MO. | |
| Apr 23, 2011 at 21:51 | comment | added | Stephan F. Kroneck | @ André Henriques: thanks for pointing out a possible source of misunderstanding; indeed, (as in the context of Galois groups with their Krull topology) the question was intended that way, i.e. that the given group structure be compatible with the profinite topology and that one has a topological group. Kind regards, Stephan. | |
| Apr 23, 2011 at 21:51 | comment | added | Stephan F. Kroneck | @ Pete L. Clark: Dear Pete, first of all thanks for your comments ! Secondly, as I'm quite new to this forum, I'm probably not aware of all the customs here - I simply gave my "generic" username when I "enrolled" here. (In particular, I wouldn't know how to "roll" the matter back ?!). At the time I didn't feel that I was doing any harm. (I stand corrected.) Thanks also for the point ! Kind regards, Stephan F. Kroneck. | |
| Apr 23, 2011 at 21:07 | comment | added | André Henriques | "non-homeomorphic"?? All (separable) profinite topologies make your group homeomorphic to a Cantor set... or do you really care about non-separable topologies? A perhaps more interesting question is to find two topologies on the same abstract group that make them non-isomorphic in the category of topological groups. | |
| Apr 23, 2011 at 19:24 | comment | added | Pete L. Clark | Dear Stephan: 1) Good question: +1. 2) If you are willing to include (part of) your name in the question anyway, you should at least consider including it in your username (e.g. something like Stephan [first letter of your surname]). This is a professional forum and -- while it's certainly not required -- a lot of us much prefer when people use (some appropriate portion of) their actual names, rather than epithets, nicknames or pseudonyms. | |
| Apr 23, 2011 at 16:28 | history | asked | Stephan F. Kroneck | CC BY-SA 3.0 |