Homology groups of types in model theory and the computation of $H_2(p)$

Abstract

We present definitions of homology groups $H_n(p)$, $n\ge 0$, 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 $H_2(p)$.