Eilenberg-MacLane complexes are generalized
to GEM complexes. This generalization is then shown to unify many diverse
seemingly unrelated concepts in low- dimensional topology. All 2-dimensional
CW-complexes , all 3-dimensional manifolds , and all smooth 2-knot
exteriors  are shown to be GEM complexes. A method is given for computing
the (co)homology of the universal cover of a GEM complex from the (co)homology
of a naturally associated group system. Hence, this yields a method for
computing the second homotopy group pi2
and the k-invariant
in H3(pi1, pi2).
(*) Partially supported by the L-O-O-P Fund.