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Title: Double complexes and vanishing of Novikov cohomology
Authors: Hüttemann, Thomas
Keywords: Torus
Truncated Product
Double Complex
Finite Domination
Novikov Cohomology
Issue Date: 2011
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 37, No 4, (2011), 295p-304p
Abstract: 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.
Description: 2010 Mathematics Subject Classification: Primary 18G35; Secondary 55U15.
ISSN: 1310-6600
Appears in Collections:Volume 37, Number 4

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