Mapping Class Group of Torus.
I am trying to understand why the mapping class group of the
torus T^2 (i.e., the group of orientation-preserving self-
diffeomorphisms, up to isotopy) is (iso. to) Gl(2,Z) ( I just
realized this is the name of the group of orientation-preserving
automorphisms). Anyone know what the connection is, between these
two.(or, even better, a proof, or ref. for a proof.)? .
All I can think off is that there may be some connection
with the fact that Pi_1(T^2)=Z(+)Z , but that is all I have.
Thanks for any Ideas.