TY - JOUR
AU - Barratt, M. G.
AB - By M. G. BARRATT [Received 20 April 1954.—Read 22 April 1954] Introduction I N a previous paper ((1), hereafter referred to as I) we defined the Track Groups (P, Q) {X, x ; x ) of a pair [P, Q], where Q is closed in P, and x is 0 0 0 a point of X, for ra ^ 1. If K is an (w+l)-dimensional CW-complex with n x but one vertex, and K ~ is its (n—l)th skeleton, we showed that the n x m m group (K,K - ) {X,XQ,x ), written (n-\-l,n— l) , is a central extension of J^+Vm+n+i) by H"(7T ), where H*{G) = H*{K,Z«-i; 0), and m+n for any space X. Here we mean by an extension of G by Q, a group E with subgroup G such that E/G = Q. In the first part of this paper (Chapter 5) we calculate this extension for a finite complex K, deducing the results (except for the commutators when m — n = 1) from the special n n n+1 cases K = S , K = S U e . It is found that the extension is non-trivial in general; for example, if 
TI - Track Groups (II)
JF - Proceedings of the London Mathematical Society
DO - 10.1112/plms/s3-5.3.285
DA - 1955-07-01
UR - https://www.deepdyve.com/lp/wiley/track-groups-ii-6817LEDuNI
SP - 285
EP - 329
VL - s3-5
IS - 3
DP - DeepDyve
ER -