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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.

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# Torelli group

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