Geodesic
Double complexes and vanishing of Novikov cohomology
Serdica Mathematical Journal, Tome 37 (2011) no. 4, pp. 295-304.

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We consider non-standard totalisation functors for double complexes, involving left or right truncated products. We show how properties of these imply that the algebraic mapping torus of a self map h of a cochain complex of finitely presented modules has trivial negative Novikov cohomology, and has trivial positive Novikov cohomology provided h is a quasi-isomorphism. As an application we obtain a new and transparent proof that a finitely dominated cochain complex over a Laurent polynomial ring has trivial (positive and negative) Novikov cohomology.
Keywords: Torus, Truncated Product, Double Complex, Finite Domination, Novikov Cohomology 
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     author = {H\"uttemann, Thomas},
     title = {Double complexes and vanishing of {Novikov} cohomology},
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Hüttemann, Thomas. Double complexes and vanishing of Novikov cohomology. Serdica Mathematical Journal, Tome 37 (2011) no. 4, pp. 295-304. http://geodesic.mathdoc.fr/item/SMJ2_2011_37_4_a2/