Track Groups (II)

IN a previous paper ((1), hereafter referred to as I) we defined the Track Groups (P, Q){X, x0; x0) of a pair [P, Q], where Q is closed in P, and x0 is a point of X, for ra ^ 1. If K is an (w+l)-dimensional CW-complex with but one vertex, and K~ is its (n—l)th skeleton, we showed that the group (K,K-){X,XQ,xQ), written (n-\-l,n— l) , is a central extension of J^+Vm+n+i) by H"(7Tm+n), where H*{G) = H*{K,Z«-i; 0), and