On the quasi-component of minimal pseudocompact abelian groups

We describe the relationship between the quasi-component q(G) of a (perfectly) minimal pseudocompact abelian group G and the quasi-component q(G∼) of its completion. Specifically, we characterize the pairs (C, A) of compact connected abelian groups C and subgroups A such that A∼= q(G) and C∼=q(G∼). As a consequence, we show that for every positive integer n or n = ω, there exist plenty of abelian pseudocompact perfectly minimal n-dimensional groups G such that the quasi-component of G is not dense in the quasi-component of the completion of G.