Double complexes and vanishing of Novikov cohomology

Hüttemann, Thomas. "Double complexes and vanishing of Novikov cohomology." Serdica Mathematical Journal 37.4 (2011): 295-304. <http://eudml.org/doc/281563>.

@article{Hüttemann2011,
abstract = {2010 Mathematics Subject Classification: Primary 18G35; Secondary 55U15.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.},
author = {Hüttemann, Thomas},
journal = {Serdica Mathematical Journal},
keywords = {Torus; Truncated Product; Double Complex; Finite Domination; Novikov Cohomology; mapping torus; truncated product; double complex; finite domination; Novikov cohomology},
language = {eng},
number = {4},
pages = {295-304},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Double complexes and vanishing of Novikov cohomology},
url = {http://eudml.org/doc/281563},
volume = {37},
year = {2011},
}

TY - JOUR
AU - Hüttemann, Thomas
TI - Double complexes and vanishing of Novikov cohomology
JO - Serdica Mathematical Journal
PY - 2011
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 37
IS - 4
SP - 295
EP - 304
AB - 2010 Mathematics Subject Classification: Primary 18G35; Secondary 55U15.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.
LA - eng
KW - Torus; Truncated Product; Double Complex; Finite Domination; Novikov Cohomology; mapping torus; truncated product; double complex; finite domination; Novikov cohomology
UR - http://eudml.org/doc/281563
ER -