We consider a non-standard totalisation functor to produce a cochain complex
from a given double complex: instead of sums or products, totalisation is
defined via truncated products of modules. We give an elementary proof of the
fact that a double complex with exact rows (resp, columns) yields an acyclic
cochain complex under totalisation using right (resp, left) truncated products.
As an application we consider the algebraic mapping torus T(h) of a self map h
of a cochain complex C. We show that if C consists of finitely presented
modules then T(h) has trivial negative Novikov cohomology; if in addition h is
a quasi-isomorphism, then T(h) has trivial positive Novikov cohomology as well.
As a consequence we obtain a new proof that a finitely dominated cochain
complex over a Laurent polynomial ring has trivial Novikov cohomology.Comment: 6 pages; diagrams typeset with Paul taylors "diagrams" macro package;
v2: 7 pages, expanded introduction, minor changes in exposition; v3: minor
changes to abstract, typos correcte
