N-Fold 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 generalise this corrected result to derive formulae of Hopf type for the n-fold Čech derived functors of the lower central series functors Z k .The paper ends with an application to algebraic K-theory.