Algebraic invariants for homotopy types
  We define inductively a sequence of purely algebraic invariants - namely, classes in the Quillen cohomology of the Pi-algebra \pi_* X - for distinguishing between different homotopy types of spaces. Another sequence of such cohomology classes allows one to decide whether a given abstract Pi-algebra can be realized as the homotopy Pi-algebra of a space in the first place.   The paper is written for a relatively general "resolution model category", so it also applies, for example, to rational homotopy types. 
David Blanc