  Let S be an oriented surface of finite type of genus g with m punctures and
where 3g-3+m>1. We show that the mapping class group M(S) of S is
quasi-isometrically rigid. We also give a different proof of the following
result of Behrstock and Minsky: The homological dimension of the asmyptotic
cone of M(S) of S equals 3g-3+m.
