1
$\begingroup$

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.

1 Answers 1

7

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.

  • 1
    Internets is okay. Try its. :)2011-06-01