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NFOLD ČECH DERIVED FUNCTORS AND GENERALISED HOPF TYPE FORMULAS
"... Abstract. In 1988, Brown and Ellis published [3] a generalised Hopf formula for the higher homology of a group. Although substantially correct, their result lacks one necessary condition. We give here a counterexample to the result without that condition. The main aim of this paper is, however, to g ..."
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Abstract. In 1988, Brown and Ellis published [3] a generalised Hopf formula for the higher homology of a group. Although substantially correct, their result lacks one necessary condition. We give here a counterexample to the result without that condition. The main aim of this paper is, however, to generalise this corrected result to derive formulae of Hopf type for the nfold Čech derived functors of the lower central series functors Zk. The paper ends with an application to algebraic Ktheory. Introduction and Summary The well known Hopf formula for the second integral homology of a group says that for a given group G there is an isomorphism H2(G) ∼ = R ∩ [F, F]
VANISHING LINE FOR THE DESCENT SPECTRAL SEQUENCE
, 2001
"... Abstract. We prove that if f: X → Y is a surjective and proper map between locally compact spaces and if additionally it is cohomologically (k −1)connected, for some k> 0, = 0 provided q < pk. then for the cohomological descent spectral sequence [1] one has E pq 2 Mathematics Subject Classifi ..."
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Abstract. We prove that if f: X → Y is a surjective and proper map between locally compact spaces and if additionally it is cohomologically (k −1)connected, for some k> 0, = 0 provided q < pk. then for the cohomological descent spectral sequence [1] one has E pq 2 Mathematics Subject Classifications (2000). 18G40, 55N30