  Many authors have constructed different, but related, linear group cocycles
that are usually referred to as ``Eisenstein cocycles.'' The main goal of this
work is to describe a topological construction that is a common source for all
these cocycles. One interesting feature of this construction is that, starting
from a purely topological class, it leads to the algebraic world of meromorphic
forms 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.''
