Timeline for What's a non-abelian totally ordered group?
Current License: CC BY-SA 4.0
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| Feb 9, 2020 at 11:34 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question has been bumped anyway)
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| Jun 22, 2013 at 15:22 | comment | added | Andy Putman | @Salvo Tringali : It's a sad but unchangeable fact of life that mathematical definitions vary from person to person (eg try getting two algebraic geometers to agree on a general definition of a generically finite morphism). It's probably not worth getting too worked up about it. I have to admit that I've never read Rolfsen's book, and thus I do not know his conventions (though mine are very common in the literature). I mostly learned the subject through conversations with Bert Wiest back when we were both at MSRI (you'll notice I'm thanked in the new edition of their book). | |
| Jun 22, 2013 at 8:41 | comment | added | Salvo Tringali | Thanks for your clarifications, but you will agree that "common usage" has a very relative meaning: In France, e.g., people are known for speaking mathematics in a quite different way than elsewhere, regardless of their area of expertise; also, you mentioned Rolfsen, and Rolfsen, for an instance, does regard the fundamental grp of $\mathbb P^2$ as a surface group (see p. 4 in the survey linked in the OP). Lastly, it's perhaps worth remarking that, in their book, Rhemtulla (you seem to have mistyped his name) and Mura use the expression "orderable group" in a different sense than in the OP. | |
| Jun 18, 2013 at 15:46 | comment | added | Andy Putman | @Salvo Tringali : To me, a surface group is the fundamental group of a closed oriented surface (I also often require that the group be nonabelian, though I'm not doing that here). This is a common usage in geometric and combinatorial group theory, though I suppose I should have explained it here. As far as Thurston goes, I have spoken to people with whom he discussed it, but I'm pretty sure that there is no written record of it and that he never gave talks about it. | |
| Jun 18, 2013 at 10:54 | comment | added | Salvo Tringali | @Andy Putman. There seems to be a minor issue here, but it is probably due to a mere question of dictionary, so let me ask: What do you mean by a surface group? More specifically, does your definition include the fundamental group of the projective plane? If so, it is not true that all surface groups are bi-orderable. On another hand, can you provide historical evidence that Thurston had discovered that braid groups are left-orderable before Dehornoy did? Thanks in advance. | |
| Nov 4, 2009 at 6:25 | vote | accept | Andrew Critch | ||
| Nov 3, 2009 at 23:33 | history | edited | Andy Putman | CC BY-SA 2.5 |
added 2 characters in body
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| Nov 3, 2009 at 23:28 | history | edited | Andy Putman | CC BY-SA 2.5 |
added 648 characters in body; added 162 characters in body
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| Nov 3, 2009 at 22:52 | history | answered | Andy Putman | CC BY-SA 2.5 |