Abstract
For this paper we define the notion of a complete filtration. With each filtered complex A we associate a “completion” A and show that A and A give rise to the same spectral sequence. For complete filtrations the relations between the spectral sequence and H(A) are much closer. Indeed we prove (97) that if f : A + B is a (filtration preserving) map of complete filtered complexes and if f induces an isomorphism E’(A) x E'(B) for some r > 1 then H(f) :H(A)-+ H(B) is an isomorphism. Thus in a sense the spectral sequence (E’(A)} determines H(A).
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