Talk:Nielsen–Thurston classification

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Bers proof[edit]

The current dynamical discussion is not clear. If/when I have time I'll rewrite it to reflect Bers' proof of Thurston's theorem. This note is just a self-reminder/invitation for somebody else to do the work. Sam nead 21:43, 17 September 2006 (UTC)

Name of page[edit]

I doubt this is a standard name for the theorem. I've generally seen it referred to as the classification of surface automorphisms, sometimes the Nielsen-Thurston classification of... etc. If I referred to Thurston's classification theorem in a talk, I would get a lot of puzzled looks, I'm sure. --169.237.31.188 21:50, 25 August 2005 (UTC)

When the result was first explained to me, it was referred to as Thustson's classification theorem with the surface homeomorphism part implicit from the conversation. So that is what I have tended to use. That same person has referred to the result in print as Thustson's classification theorem of surface homeomorphisms. I checked Mathematical Review and the expression Thurston's classification theorem shows up in 11 reviews and Thurston's classification of surface ... shows up 12 times. Nielsen's name shows up with Thurston's in a few reviews. Maybe we should avoid the ellipsis and change the article to Thustson's classification theorem for surface homeomorphisms. XaosBits 03:36, 26 August 2005 (UTC)
Hi, sorry, I was logged out when I wrote the above comment. Anyway, I wonder how you did this search. When I searched Math Reviews (via MathSciNet), I did get 11 hits for "Thurston's classification theorem", but not as a single phrase, e.g. one review explicitly called it the Nielsen-Thurston classification (the word "theorem" was elsewhere in the review...). Another mentioned "Thurston's classification theorem for isotopy classes of surface homeomorphisms", not just the title of this article per se. As much as half of them or so refer to the Nielsen-Thurston classification theorem. Anyway, I get 19 hits for Nielsen-Thurston classification, and when I checked (correctly I believe), that showed up as a phrase. None of the reviews I found refer to it just as "Thurston's classification theorem", which was (and is still) my contention. --C S 00:38, 31 October 2005 (UTC)
You think the name would generate puzzled looks? I suppose I would call it "Thurston's classification of surface homeomorphisms" if I were giving a talk or writing a new wiki article, but I would know what someone meant if they just said "Thurston's classification theorem". Also note that Thurston has a paper on these matters called "New proofs of some results of Nielsen", and the MathSciNet review for that paper begins:
The paper can equally well be entitled "New proofs of some results of Thurston".
--David Dumas 02:33, 4 September 2005 (UTC)
Right, my contention is that you would use some phrasing as you said. Using unusual terminology would indeed generate puzzled looks, don't you agree? You would know what is meant, given the right context, but I think that for an encyclopedia article we would be very precise and unambiguous as possible. Not only that, but we should use "correct"/usual terminology. This is even more important in a wiki, since we want to make it easy for people to create links. For example, a related case that came up was when the geometrization conjecture article had the title "Thurston's conjecture". That's not the usual way of referring to the conjecture, but in a talk, I'm sure I would know from context what was meant.
I'm not really sure why you brought up Thurston's paper. I definitely am not denying Thurston's contributions, if that is what you are thinking. If you don't think Nielsen should be credited, I'm curious as to why you think that. In any case, it's definitely not Wikipedia's role to correct injustice in naming conventions or whatnot by using different terminology.
I propose the article be moved to Nielsen-Thurston classification. Not only is it short, but I bet many people use this term and it will be as unambiguous as possible. --C S 00:38, 31 October 2005 (UTC)
I would call this the Thurston classification of surface automorphisms. Why not include Nielsen? Because he didn't have a clue about the pseudo-Anosov case. The title of Casson's book is being quite generous. Sam nead 02:42, 31 October 2005 (UTC)
It's not just Casson that is being "quite generous". But that's beside the point! I think Nielsen-Thurston classification is just as common a name, if not more so, than Thurston classification. Do you disagree? Or are you basing your decision on who you think is deserving or not? The former is a valid reason, the latter is not. Casson-Bleiler is a pretty famous book...I suspect it's one big reason for the popularity of the terminology "Nielsen-Thurston classification". --C S 03:26, 31 October 2005 (UTC)
This is an aside to this discussion, but I'm curious as to whether you came to your conclusions about Nielsen from having read his work and/or the work by others such as Gilman (and that Handel and Thurston paper referenced above), which I believe do the classification using tools Nielsen developed. I always thought that the point of geodesic laminations was to make Thurston's theory more "Nielsen-like". I'm really not qualified at all to judge this issue, but I always got the impression from my teachers that Nielsen knew quite a bit and later much, including very interesting examples of the classification, was rediscovered in his old papers. --C S 18:55, 31 October 2005 (UTC)
I am not opposed to crediting Nielsen, and agree that wikipedia is not the place to correct injustice in naming conventions. In my earlier comments I was mainly addressing the issue of how much detail (and not necessarily which names) should be included in the title of the article. I say either change the title to "Nielsen-Thurston classification" outright, or put it to a vote. --David Dumas 23:19, 1 November 2005 (UTC)
"Nielsen-Thurston classification" is fine with me. It is much clearer than "Thurston classification" if not as clear as "Classification of surface automorphisms" (even without credit to any one person being given). I guess if Casson credits Nielsen then who are we to say "no"? As an aside: I have looked thru Stillwell's translations of some of Nielsen's papers. There is a lot of stuff that looks like group theory and there is some dynamics on the boundary of the hyperbolic plane. But I don't recall any geodesic laminations -- I believe that those are Thurston's innovation, as a neater tool than train tracks (which were invented by Bob Edwards and reinvented by Thurston (as long as we are keeping score)). Sam nead 00:09, 2 November 2005 (UTC)
that's interesting...I had no idea Edwards invented train tracks before Thurston. --C S 00:39, 2 November 2005 (UTC)
Gah - my mistake -- not Bob Edwards, but rather Bob (Robert) Williams. He called them "branched manifolds". His home page is http://www.ma.utexas.edu/~bob/. best, Sam nead 16:57, 2 November 2005 (UTC)

Ok, if nobody objects then, for the reasons stated above (1. frequency of use 2. shortness of term), I will move the page to Nielsen-Thurston classification. I will wait a week or so first, so voice your objections, if any. --C S 00:39, 2 November 2005 (UTC)

No objections. Better title. XaosBits 05:19, 2 November 2005 (UTC)
Sounds good. Most of the titles proposed in the above discussion can be redirects. JPB 16:34, 2 November 2005 (UTC)

Phew! I've moved the page and created redirects based on names mentioned above. You can use the 'what links here' link in the toolbox menu to see the redirects. --C S 23:52, 11 November 2005 (UTC)