Combinatorial Homotopy and 4-Dimensional Complexes.

This book by Baues handles the classification of 4-dimensional complexes. Henry Whitehead commented in his famous paper, Combinatorial homotopy I, (1949), ‘What has been achieved so far is a purely algebraic description of the homotopy type of any 3-dimensional complex and of any finite, simply connected 4-dimensional complex.’ (This case of simply connected 4-dimensional complexes had been treated by him in another paper in that same year of 1949.) This book by Baues gives a solution in the non-simply connected case.