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Manifold: what's the meaning of this name?

  1. Dec 2, 2009 #1
    Dear all,
    I've always wondered where the name "manifold" comes from?
    Any idea?
  2. jcsd
  3. Dec 2, 2009 #2
  4. Dec 2, 2009 #3

    Thanks, maybe my question was not clear. The question is why was that word, "manifold", with those meanings (see your link) used to label this topological space
  5. Dec 2, 2009 #4
    I think it come from the fact that one of the meanings is a 'thing with several possible shapes'. A bare manifold is essentially that, a thing you can add structure too or deform into several possible shapes. At least that's my understanding of this.
  6. Dec 2, 2009 #5


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    Riemann, who was the first to talk of manifolds, called them (in german!) something like "multiply extended quantities"... probably having in mind that they would be objects who could locally be parametrized by many coordinates... a natural generalization of surfaces.
    If "manifold" is not as good a translation of the word Riemann used for them as "multiply extended quantities" is, at least it has the merit of being brief!
  7. Dec 2, 2009 #6
    So the English usage in mathematics is as a translation of the German "Mannigfaltigkeit"
  8. Dec 8, 2009 #7
    The first time I saw it I mistook it for "mainfold",haha
  9. Dec 9, 2009 #8


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    Hi Goldbeetle! Hi g_edgar! :smile:
    "mannigfaltig" seems to be the German for "diverse" "various" or "multifarious",

    and "mannigfaltigkeit" for "diversity" "variety" or "manifoldness".

    At http://en.wikipedia.org/wiki/User:Markus_Schmaus/Riemann" [Broken], Markus Schmaus says …
    … and illustrates this with German quotations (and his own English translations) from Riemann's http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Geom/" [Broken]
    Last edited by a moderator: May 4, 2017
  10. Dec 10, 2009 #9


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    I have always assumed that "manifold" was associated with "many dimensions".
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