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arxiv: math/0303050 · v1 · submitted 2003-03-05 · 🧮 math.KT · math.CT

N-Fold Cech Derived Functors and Generalised Hopf Type Formulas

classification 🧮 math.KT math.CT
keywords functorshopfresultcechconditionderivedgeneralisedn-fold
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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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