Given a finite connected –complex with cohomological dimension 2, we show it may be constructed up to homotopy by applying the Quillen plus construction to the Cayley complex of a finite group presentation. This reduces the D(2) problem to a question about perfect normal subgroups.
"Quillen's plus construction and the D(2) problem." Algebr. Geom. Topol. 9 (3) 1399 - 1411, 2009. https://doi.org/10.2140/agt.2009.9.1399