Homology Groups of Types in Model Theory and the Computation of H 2 ( p )

We present definitions of homology groups H n ( p ), n ≥ 0, associated to a complete type p . We show that if the generalized amalgamation properties hold, then the homology groups are trivial. We compute the group H 2 ( p ) for strong types in stable theories and show that any profinite abelian group can occur as the group H 2 ( p ).