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N-Fold Cech Derived Functors and Generalised Hopf Type Formulas

Guram Donadze·Nick Inassaridze·Timothy Porter
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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 n-fold Cech derived functors of the lower central series functors Z_k. The paper ends with an application to algebraic K-theory.

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Guram Donadze, Nick Inassaridze, Timothy Porter. 2003-03-05. N-Fold Cech Derived Functors and Generalised Hopf Type Formulas. https://arxiv.org/abs/math/0303050

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