On Levin's generalization of the plus construction
  We present a proof of the following theorem of Levin: For every connected CW complex $K$ there is a simply connected CW complex $K^+$ obtained from $K$ by attaching cells of dimension 2 and 3 such that the inclusion $K\to K^+$ induces isomorphisms of homology groups in dimension $>1$. 
Alexandr Dranishnikov
math.AT