Is there a finite generating set for the Torelli group $T_2$?

D.Johnson showed in 1983 that for g>2 , the Torelli group $Tg$ has a finite set of generators. I have not been able to find out what the case is for g=1,2; does anyone know of any result for generating sets for these cases (i.e., are there finite generating sets for g=1,2)?

Thanks.

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1 Answer

In the genus 1 case, the Torelli group is trivial. This is a classical result, see for example Birman's book.

In the genus 2 case, the Torelli group is an infinitely-generated free group. This is a theorem of Geoff Mess. A google search will give you a precise reference.

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Thanks, Ryan. When I finally get my act together and figure out how to sign-in, I will give you (and all others) points for your answers. (By then, I will have figured out how this "series of tubes" called the internets works). – gary Jun 1 '11 at 1:35
Internets is okay. Try its. :) – Ryan Budney Jun 1 '11 at 1:38