  We present a homological characterisation of those chain complexes of modules
over a Laurent polynomial ring in several indeterminates which are finitely
dominated over the ground ring (that is, are a retract up to homotopy of a
bounded complex of finitely generated free modules). The main tools, which we
develop in the paper, are a non-standard totalisation construction for
multi-complexes based on truncated products, and a high-dimensional mapping
torus construction employing a theory of cubical diagrams that commute up to
specified coherent homotopies.
