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Many authors have constructed different, but related, linear group cocyclesthat are usually referred to as ``Eisenstein cocycles.'' The main goal of thiswork is to describe a topological construction that is a common source for allthese cocycles. One interesting feature of this construction is that, startingfrom a purely topological class, it leads to the algebraic world of meromorphicforms on hyperplane complements in $n$-fold products of either the (complex)additive group, the multiplicative group or a (family of) elliptic curve(s).This yields the construction of three types of ``Sczech cocycles.''

Cocycles de groupe pour GL$_n$ et arrangements d'hyperplans