ON ZEEMAN FILTRATION IN HOMOLOGY

For a finite complex K, Zeeman constructed a spectral sequence, converging to the homology of the complex, of the form E2pq = H(q)(K; H(p)) double-line arrow pointing right H(p-q)(K). Special attention was given to the corresponding filtration in the homology of K, essentially dependent on the cohomology: H(r)(K) = F0H(r)(K) superset-of F1H(r)(K) superset-of ... superset-of F(q)H(r)(K) superset-of ... , E(infinity)pq = F(q)H(r)(K)/F(q+1)H(r)(K), r = p - q, where H(p) is the coefficient system determined by the local homology groups H(p)x = H(p)(K, K\x). The object of the present paper is to show that the Zeeman filtration, although defined in terms of the simplicial structure of the complex, is, in the end, of a general-categorical nature. Due to this fact, a more complete description of its connection with the topology of the space and with the product is obtained. Bibliography: 19 titles.