V H complexes, towers and subgroups of F x F

Let F be a free group. We explain the classification of finitely presented subgroups of F x F in geometric terms. The classification emerges as a spec ial case of results concerning the structure of 2-complexes which are built out of squares and have the property that the link of each vertex has no r educed circuits whose length is odd or less than four. We obtain these resu lts using tower arguments and elements of the theory of non-positively curv ed spaces.