We consider a functor from the category of groups to itself, , that we call right exact –completion of a group. It is connected with the pro-nilpotent completion by the short exact sequence , where is Baer invariant of . We prove that is an invariant of homological equivalence of a space . Moreover, we prove an analogue of Stallings’ theorem: if is a –connected group homomorphism, then . We give examples of –manifolds and such that but . We prove that for a group with finitely generated we have . So the difference between and lies in . This allows us to treat as a transfinite invariant of . The advantage of our approach is that it can be used not only for –manifolds but for arbitrary spaces.
"Right exact group completion as a transfinite invariant of homology equivalence." Algebr. Geom. Topol. 21 (1) 447 - 468, 2021. https://doi.org/10.2140/agt.2021.21.447