Homology of Group Systems with Applications to Low Dimensional Topology 



Samuel J. Lomonaco, Jr. (*)


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 [1], all 3-dimensional manifolds [5], and all smooth 2-knot exteriors [5] 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.