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Torelli group

  1. Oct 11, 2006 #1

    While reading the lectures of Luest and Theisen on string
    theory I encountered the Torelli group. They are very vague
    about it (the discussion is at pages 118-119) but they say
    that it correspond to twists arround trivial cycles so the
    homology basis is unchanged but these transformations
    are non-trivial diffeomorphisms nevertheless.

    I searched the Web for some drawing describing these
    twists but I couldn't find them. Would some kind soul
    explain them to me? I *think* that they should be like the
    Dehn twists but I'm not sure about that.

    There's some other interesting piece of information in
    Luest & Theisen about the moduli space of genus g Riemann
    surfaces. It seems that this moduli space gets quite
    complicated for genus g > 3. I think g=3 is the state
    of the art in computing superstring amplitudes (I have no
    idea about bosonic string amplitudes). I therefore think it's
    necessary to go at least to g=4 to see if there's something
    qualitatively different there.
  2. jcsd
  3. Oct 11, 2006 #2
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